<?php
namespace PhpOffice\PhpSpreadsheet\Calculation;
< use PhpOffice\PhpSpreadsheet\Shared\Trend\Trend;
> use PhpOffice\PhpSpreadsheet\Calculation\Statistical\Averages;
> use PhpOffice\PhpSpreadsheet\Calculation\Statistical\Conditional;
> use PhpOffice\PhpSpreadsheet\Calculation\Statistical\Confidence;
> use PhpOffice\PhpSpreadsheet\Calculation\Statistical\Counts;
> use PhpOffice\PhpSpreadsheet\Calculation\Statistical\Maximum;
> use PhpOffice\PhpSpreadsheet\Calculation\Statistical\Minimum;
> use PhpOffice\PhpSpreadsheet\Calculation\Statistical\Permutations;
> use PhpOffice\PhpSpreadsheet\Calculation\Statistical\StandardDeviations;
> use PhpOffice\PhpSpreadsheet\Calculation\Statistical\Trends;
> use PhpOffice\PhpSpreadsheet\Calculation\Statistical\Variances;
> /**
class Statistical
> * @deprecated 1.18.0
{
> */
const LOG_GAMMA_X_MAX_VALUE = 2.55e305;
< const XMININ = 2.23e-308;
const EPS = 2.22e-16;
const MAX_VALUE = 1.2e308;
< const MAX_ITERATIONS = 256;
const SQRT2PI = 2.5066282746310005024157652848110452530069867406099;
< private static function checkTrendArrays(&$array1, &$array2)
< {
< if (!is_array($array1)) {
< $array1 = [$array1];
< }
< if (!is_array($array2)) {
< $array2 = [$array2];
< }
<
< $array1 = Functions::flattenArray($array1);
< $array2 = Functions::flattenArray($array2);
< foreach ($array1 as $key => $value) {
< if ((is_bool($value)) || (is_string($value)) || ($value === null)) {
< unset($array1[$key], $array2[$key]);
< }
< }
< foreach ($array2 as $key => $value) {
< if ((is_bool($value)) || (is_string($value)) || ($value === null)) {
< unset($array1[$key], $array2[$key]);
< }
< }
< $array1 = array_merge($array1);
< $array2 = array_merge($array2);
<
< return true;
< }
<
< /**
< * Incomplete beta function.
< *
< * @author Jaco van Kooten
< * @author Paul Meagher
< *
< * The computation is based on formulas from Numerical Recipes, Chapter 6.4 (W.H. Press et al, 1992).
< *
< * @param mixed $x require 0<=x<=1
< * @param mixed $p require p>0
< * @param mixed $q require q>0
< *
< * @return float 0 if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow
< */
< private static function incompleteBeta($x, $p, $q)
< {
< if ($x <= 0.0) {
< return 0.0;
< } elseif ($x >= 1.0) {
< return 1.0;
< } elseif (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > self::LOG_GAMMA_X_MAX_VALUE)) {
< return 0.0;
< }
< $beta_gam = exp((0 - self::logBeta($p, $q)) + $p * log($x) + $q * log(1.0 - $x));
< if ($x < ($p + 1.0) / ($p + $q + 2.0)) {
< return $beta_gam * self::betaFraction($x, $p, $q) / $p;
< }
<
< return 1.0 - ($beta_gam * self::betaFraction(1 - $x, $q, $p) / $q);
< }
<
< // Function cache for logBeta function
< private static $logBetaCacheP = 0.0;
<
< private static $logBetaCacheQ = 0.0;
<
< private static $logBetaCacheResult = 0.0;
<
< /**
< * The natural logarithm of the beta function.
< *
< * @param mixed $p require p>0
< * @param mixed $q require q>0
< *
< * @return float 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
< *
< * @author Jaco van Kooten
< */
< private static function logBeta($p, $q)
< {
< if ($p != self::$logBetaCacheP || $q != self::$logBetaCacheQ) {
< self::$logBetaCacheP = $p;
< self::$logBetaCacheQ = $q;
< if (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > self::LOG_GAMMA_X_MAX_VALUE)) {
< self::$logBetaCacheResult = 0.0;
< } else {
< self::$logBetaCacheResult = self::logGamma($p) + self::logGamma($q) - self::logGamma($p + $q);
< }
< }
<
< return self::$logBetaCacheResult;
< }
<
< /**
< * Evaluates of continued fraction part of incomplete beta function.
< * Based on an idea from Numerical Recipes (W.H. Press et al, 1992).
< *
< * @author Jaco van Kooten
< *
< * @param mixed $x
< * @param mixed $p
< * @param mixed $q
< *
< * @return float
< */
< private static function betaFraction($x, $p, $q)
< {
< $c = 1.0;
< $sum_pq = $p + $q;
< $p_plus = $p + 1.0;
< $p_minus = $p - 1.0;
< $h = 1.0 - $sum_pq * $x / $p_plus;
< if (abs($h) < self::XMININ) {
< $h = self::XMININ;
< }
< $h = 1.0 / $h;
< $frac = $h;
< $m = 1;
< $delta = 0.0;
< while ($m <= self::MAX_ITERATIONS && abs($delta - 1.0) > Functions::PRECISION) {
< $m2 = 2 * $m;
< // even index for d
< $d = $m * ($q - $m) * $x / (($p_minus + $m2) * ($p + $m2));
< $h = 1.0 + $d * $h;
< if (abs($h) < self::XMININ) {
< $h = self::XMININ;
< }
< $h = 1.0 / $h;
< $c = 1.0 + $d / $c;
< if (abs($c) < self::XMININ) {
< $c = self::XMININ;
< }
< $frac *= $h * $c;
< // odd index for d
< $d = -($p + $m) * ($sum_pq + $m) * $x / (($p + $m2) * ($p_plus + $m2));
< $h = 1.0 + $d * $h;
< if (abs($h) < self::XMININ) {
< $h = self::XMININ;
< }
< $h = 1.0 / $h;
< $c = 1.0 + $d / $c;
< if (abs($c) < self::XMININ) {
< $c = self::XMININ;
< }
< $delta = $h * $c;
< $frac *= $delta;
< ++$m;
< }
<
< return $frac;
< }
<
< /**
< * logGamma function.
< *
< * @version 1.1
< *
< * @author Jaco van Kooten
< *
< * Original author was Jaco van Kooten. Ported to PHP by Paul Meagher.
< *
< * The natural logarithm of the gamma function. <br />
< * Based on public domain NETLIB (Fortran) code by W. J. Cody and L. Stoltz <br />
< * Applied Mathematics Division <br />
< * Argonne National Laboratory <br />
< * Argonne, IL 60439 <br />
< * <p>
< * References:
< * <ol>
< * <li>W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for the Natural
< * Logarithm of the Gamma Function,' Math. Comp. 21, 1967, pp. 198-203.</li>
< * <li>K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May, 1969.</li>
< * <li>Hart, Et. Al., Computer Approximations, Wiley and sons, New York, 1968.</li>
< * </ol>
< * </p>
< * <p>
< * From the original documentation:
< * </p>
< * <p>
< * This routine calculates the LOG(GAMMA) function for a positive real argument X.
< * Computation is based on an algorithm outlined in references 1 and 2.
< * The program uses rational functions that theoretically approximate LOG(GAMMA)
< * to at least 18 significant decimal digits. The approximation for X > 12 is from
< * reference 3, while approximations for X < 12.0 are similar to those in reference
< * 1, but are unpublished. The accuracy achieved depends on the arithmetic system,
< * the compiler, the intrinsic functions, and proper selection of the
< * machine-dependent constants.
< * </p>
< * <p>
< * Error returns: <br />
< * The program returns the value XINF for X .LE. 0.0 or when overflow would occur.
< * The computation is believed to be free of underflow and overflow.
< * </p>
< *
< * @return float MAX_VALUE for x < 0.0 or when overflow would occur, i.e. x > 2.55E305
< */
<
< // Function cache for logGamma
< private static $logGammaCacheResult = 0.0;
<
< private static $logGammaCacheX = 0.0;
<
< private static function logGamma($x)
< {
< // Log Gamma related constants
< static $lg_d1 = -0.5772156649015328605195174;
< static $lg_d2 = 0.4227843350984671393993777;
< static $lg_d4 = 1.791759469228055000094023;
<
< static $lg_p1 = [
< 4.945235359296727046734888,
< 201.8112620856775083915565,
< 2290.838373831346393026739,
< 11319.67205903380828685045,
< 28557.24635671635335736389,
< 38484.96228443793359990269,
< 26377.48787624195437963534,
< 7225.813979700288197698961,
< ];
< static $lg_p2 = [
< 4.974607845568932035012064,
< 542.4138599891070494101986,
< 15506.93864978364947665077,
< 184793.2904445632425417223,
< 1088204.76946882876749847,
< 3338152.967987029735917223,
< 5106661.678927352456275255,
< 3074109.054850539556250927,
< ];
< static $lg_p4 = [
< 14745.02166059939948905062,
< 2426813.369486704502836312,
< 121475557.4045093227939592,
< 2663432449.630976949898078,
< 29403789566.34553899906876,
< 170266573776.5398868392998,
< 492612579337.743088758812,
< 560625185622.3951465078242,
< ];
< static $lg_q1 = [
< 67.48212550303777196073036,
< 1113.332393857199323513008,
< 7738.757056935398733233834,
< 27639.87074403340708898585,
< 54993.10206226157329794414,
< 61611.22180066002127833352,
< 36351.27591501940507276287,
< 8785.536302431013170870835,
< ];
< static $lg_q2 = [
< 183.0328399370592604055942,
< 7765.049321445005871323047,
< 133190.3827966074194402448,
< 1136705.821321969608938755,
< 5267964.117437946917577538,
< 13467014.54311101692290052,
< 17827365.30353274213975932,
< 9533095.591844353613395747,
< ];
< static $lg_q4 = [
< 2690.530175870899333379843,
< 639388.5654300092398984238,
< 41355999.30241388052042842,
< 1120872109.61614794137657,
< 14886137286.78813811542398,
< 101680358627.2438228077304,
< 341747634550.7377132798597,
< 446315818741.9713286462081,
< ];
< static $lg_c = [
< -0.001910444077728,
< 8.4171387781295e-4,
< -5.952379913043012e-4,
< 7.93650793500350248e-4,
< -0.002777777777777681622553,
< 0.08333333333333333331554247,
< 0.0057083835261,
< ];
<
< // Rough estimate of the fourth root of logGamma_xBig
< static $lg_frtbig = 2.25e76;
< static $pnt68 = 0.6796875;
<
< if ($x == self::$logGammaCacheX) {
< return self::$logGammaCacheResult;
< }
< $y = $x;
< if ($y > 0.0 && $y <= self::LOG_GAMMA_X_MAX_VALUE) {
< if ($y <= self::EPS) {
< $res = -log($y);
< } elseif ($y <= 1.5) {
< // ---------------------
< // EPS .LT. X .LE. 1.5
< // ---------------------
< if ($y < $pnt68) {
< $corr = -log($y);
< $xm1 = $y;
< } else {
< $corr = 0.0;
< $xm1 = $y - 1.0;
< }
< if ($y <= 0.5 || $y >= $pnt68) {
< $xden = 1.0;
< $xnum = 0.0;
< for ($i = 0; $i < 8; ++$i) {
< $xnum = $xnum * $xm1 + $lg_p1[$i];
< $xden = $xden * $xm1 + $lg_q1[$i];
< }
< $res = $corr + $xm1 * ($lg_d1 + $xm1 * ($xnum / $xden));
< } else {
< $xm2 = $y - 1.0;
< $xden = 1.0;
< $xnum = 0.0;
< for ($i = 0; $i < 8; ++$i) {
< $xnum = $xnum * $xm2 + $lg_p2[$i];
< $xden = $xden * $xm2 + $lg_q2[$i];
< }
< $res = $corr + $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
< }
< } elseif ($y <= 4.0) {
< // ---------------------
< // 1.5 .LT. X .LE. 4.0
< // ---------------------
< $xm2 = $y - 2.0;
< $xden = 1.0;
< $xnum = 0.0;
< for ($i = 0; $i < 8; ++$i) {
< $xnum = $xnum * $xm2 + $lg_p2[$i];
< $xden = $xden * $xm2 + $lg_q2[$i];
< }
< $res = $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
< } elseif ($y <= 12.0) {
< // ----------------------
< // 4.0 .LT. X .LE. 12.0
< // ----------------------
< $xm4 = $y - 4.0;
< $xden = -1.0;
< $xnum = 0.0;
< for ($i = 0; $i < 8; ++$i) {
< $xnum = $xnum * $xm4 + $lg_p4[$i];
< $xden = $xden * $xm4 + $lg_q4[$i];
< }
< $res = $lg_d4 + $xm4 * ($xnum / $xden);
< } else {
< // ---------------------------------
< // Evaluate for argument .GE. 12.0
< // ---------------------------------
< $res = 0.0;
< if ($y <= $lg_frtbig) {
< $res = $lg_c[6];
< $ysq = $y * $y;
< for ($i = 0; $i < 6; ++$i) {
< $res = $res / $ysq + $lg_c[$i];
< }
< $res /= $y;
< $corr = log($y);
< $res = $res + log(self::SQRT2PI) - 0.5 * $corr;
< $res += $y * ($corr - 1.0);
< }
< }
< } else {
< // --------------------------
< // Return for bad arguments
< // --------------------------
< $res = self::MAX_VALUE;
< }
< // ------------------------------
< // Final adjustments and return
< // ------------------------------
< self::$logGammaCacheX = $x;
< self::$logGammaCacheResult = $res;
<
< return $res;
< }
<
< //
< // Private implementation of the incomplete Gamma function
< //
< private static function incompleteGamma($a, $x)
< {
< static $max = 32;
< $summer = 0;
< for ($n = 0; $n <= $max; ++$n) {
< $divisor = $a;
< for ($i = 1; $i <= $n; ++$i) {
< $divisor *= ($a + $i);
< }
< $summer += ($x ** $n / $divisor);
< }
<
< return $x ** $a * exp(0 - $x) * $summer;
< }
<
< //
< // Private implementation of the Gamma function
< //
< private static function gamma($data)
< {
< if ($data == 0.0) {
< return 0;
< }
<
< static $p0 = 1.000000000190015;
< static $p = [
< 1 => 76.18009172947146,
< 2 => -86.50532032941677,
< 3 => 24.01409824083091,
< 4 => -1.231739572450155,
< 5 => 1.208650973866179e-3,
< 6 => -5.395239384953e-6,
< ];
<
< $y = $x = $data;
< $tmp = $x + 5.5;
< $tmp -= ($x + 0.5) * log($tmp);
<
< $summer = $p0;
< for ($j = 1; $j <= 6; ++$j) {
< $summer += ($p[$j] / ++$y);
< }
<
< return exp(0 - $tmp + log(self::SQRT2PI * $summer / $x));
< }
<
< /*
< * inverse_ncdf.php
< * -------------------
< * begin : Friday, January 16, 2004
< * copyright : (C) 2004 Michael Nickerson
< * email : nickersonm@yahoo.com
< *
< */
< private static function inverseNcdf($p)
< {
< // Inverse ncdf approximation by Peter J. Acklam, implementation adapted to
< // PHP by Michael Nickerson, using Dr. Thomas Ziegler's C implementation as
< // a guide. http://home.online.no/~pjacklam/notes/invnorm/index.html
< // I have not checked the accuracy of this implementation. Be aware that PHP
< // will truncate the coeficcients to 14 digits.
<
< // You have permission to use and distribute this function freely for
< // whatever purpose you want, but please show common courtesy and give credit
< // where credit is due.
<
< // Input paramater is $p - probability - where 0 < p < 1.
<
< // Coefficients in rational approximations
< static $a = [
< 1 => -3.969683028665376e+01,
< 2 => 2.209460984245205e+02,
< 3 => -2.759285104469687e+02,
< 4 => 1.383577518672690e+02,
< 5 => -3.066479806614716e+01,
< 6 => 2.506628277459239e+00,
< ];
<
< static $b = [
< 1 => -5.447609879822406e+01,
< 2 => 1.615858368580409e+02,
< 3 => -1.556989798598866e+02,
< 4 => 6.680131188771972e+01,
< 5 => -1.328068155288572e+01,
< ];
<
< static $c = [
< 1 => -7.784894002430293e-03,
< 2 => -3.223964580411365e-01,
< 3 => -2.400758277161838e+00,
< 4 => -2.549732539343734e+00,
< 5 => 4.374664141464968e+00,
< 6 => 2.938163982698783e+00,
< ];
<
< static $d = [
< 1 => 7.784695709041462e-03,
< 2 => 3.224671290700398e-01,
< 3 => 2.445134137142996e+00,
< 4 => 3.754408661907416e+00,
< ];
<
< // Define lower and upper region break-points.
< $p_low = 0.02425; //Use lower region approx. below this
< $p_high = 1 - $p_low; //Use upper region approx. above this
<
< if (0 < $p && $p < $p_low) {
< // Rational approximation for lower region.
< $q = sqrt(-2 * log($p));
<
< return ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
< (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
< } elseif ($p_low <= $p && $p <= $p_high) {
< // Rational approximation for central region.
< $q = $p - 0.5;
< $r = $q * $q;
<
< return ((((($a[1] * $r + $a[2]) * $r + $a[3]) * $r + $a[4]) * $r + $a[5]) * $r + $a[6]) * $q /
< ((((($b[1] * $r + $b[2]) * $r + $b[3]) * $r + $b[4]) * $r + $b[5]) * $r + 1);
< } elseif ($p_high < $p && $p < 1) {
< // Rational approximation for upper region.
< $q = sqrt(-2 * log(1 - $p));
<
< return -((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
< (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
< }
< // If 0 < p < 1, return a null value
< return Functions::NULL();
< }
<
< /**
< * MS Excel does not count Booleans if passed as cell values, but they are counted if passed as literals.
< * OpenOffice Calc always counts Booleans.
< * Gnumeric never counts Booleans.
< *
< * @param mixed $arg
< * @param mixed $k
< *
< * @return int|mixed
< */
< private static function testAcceptedBoolean($arg, $k)
< {
< if (
< (is_bool($arg)) &&
< ((!Functions::isCellValue($k) && (Functions::getCompatibilityMode() === Functions::COMPATIBILITY_EXCEL)) ||
< (Functions::getCompatibilityMode() === Functions::COMPATIBILITY_OPENOFFICE))
< ) {
< $arg = (int) $arg;
< }
<
< return $arg;
< }
<
< /**
< * @param mixed $arg
< * @param mixed $k
< *
< * @return bool
< */
< private static function isAcceptedCountable($arg, $k)
< {
< if (
< ((is_numeric($arg)) && (!is_string($arg))) ||
< ((is_numeric($arg)) && (!Functions::isCellValue($k)) &&
< (Functions::getCompatibilityMode() !== Functions::COMPATIBILITY_GNUMERIC))
< ) {
< return true;
< }
<
< return false;
< }
<
/**
* AVEDEV.
*
* Returns the average of the absolute deviations of data points from their mean.
* AVEDEV is a measure of the variability in a data set.
*
* Excel Function:
* AVEDEV(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\Averages::averageDeviations()
* @return float|string
> * Use the averageDeviations() method in the Statistical\Averages class instead
*/
> *
public static function AVEDEV(...$args)
{
< $aArgs = Functions::flattenArrayIndexed($args);
<
< // Return value
< $returnValue = 0;
<
< $aMean = self::AVERAGE(...$args);
< if ($aMean === Functions::DIV0()) {
< return Functions::NAN();
< } elseif ($aMean === Functions::VALUE()) {
< return Functions::VALUE();
< }
<
< $aCount = 0;
< foreach ($aArgs as $k => $arg) {
< $arg = self::testAcceptedBoolean($arg, $k);
< // Is it a numeric value?
< // Strings containing numeric values are only counted if they are string literals (not cell values)
< // and then only in MS Excel and in Open Office, not in Gnumeric
< if ((is_string($arg)) && (!is_numeric($arg)) && (!Functions::isCellValue($k))) {
< return Functions::VALUE();
< }
< if (self::isAcceptedCountable($arg, $k)) {
< $returnValue += abs($arg - $aMean);
< ++$aCount;
< }
< }
<
< // Return
< if ($aCount === 0) {
< return Functions::DIV0();
< }
<
< return $returnValue / $aCount;
> return Averages::averageDeviations(...$args);
}
/**
* AVERAGE.
*
* Returns the average (arithmetic mean) of the arguments
*
* Excel Function:
* AVERAGE(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\Averages::average()
* @return float|string
> * Use the average() method in the Statistical\Averages class instead
*/
> *
public static function AVERAGE(...$args)
{
< $returnValue = $aCount = 0;
<
< // Loop through arguments
< foreach (Functions::flattenArrayIndexed($args) as $k => $arg) {
< $arg = self::testAcceptedBoolean($arg, $k);
< // Is it a numeric value?
< // Strings containing numeric values are only counted if they are string literals (not cell values)
< // and then only in MS Excel and in Open Office, not in Gnumeric
< if ((is_string($arg)) && (!is_numeric($arg)) && (!Functions::isCellValue($k))) {
< return Functions::VALUE();
< }
< if (self::isAcceptedCountable($arg, $k)) {
< $returnValue += $arg;
< ++$aCount;
< }
< }
<
< // Return
< if ($aCount > 0) {
< return $returnValue / $aCount;
< }
<
< return Functions::DIV0();
> return Averages::average(...$args);
}
/**
* AVERAGEA.
*
* Returns the average of its arguments, including numbers, text, and logical values
*
* Excel Function:
* AVERAGEA(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\Averages::averageA()
* @return float|string
> * Use the averageA() method in the Statistical\Averages class instead
*/
> *
public static function AVERAGEA(...$args)
{
< $returnValue = null;
<
< $aCount = 0;
< // Loop through arguments
< foreach (Functions::flattenArrayIndexed($args) as $k => $arg) {
< if (
< (is_bool($arg)) &&
< (!Functions::isMatrixValue($k))
< ) {
< } else {
< if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
< if (is_bool($arg)) {
< $arg = (int) $arg;
< } elseif (is_string($arg)) {
< $arg = 0;
< }
< $returnValue += $arg;
< ++$aCount;
< }
< }
< }
<
< if ($aCount > 0) {
< return $returnValue / $aCount;
< }
<
< return Functions::DIV0();
> return Averages::averageA(...$args);
}
/**
* AVERAGEIF.
*
* Returns the average value from a range of cells that contain numbers within the list of arguments
*
* Excel Function:
* AVERAGEIF(value1[,value2[, ...]],condition)
*
< * @param mixed $aArgs Data values
> * @Deprecated 1.17.0
> *
> * @see Statistical\Conditional::AVERAGEIF()
> * Use the AVERAGEIF() method in the Statistical\Conditional class instead
> *
> * @param mixed $range Data values
* @param string $condition the criteria that defines which cells will be checked
< * @param mixed[] $averageArgs Data values
> * @param mixed[] $averageRange Data values
*
< * @return float|string
> * @return null|float|string
*/
< public static function AVERAGEIF($aArgs, $condition, $averageArgs = [])
> public static function AVERAGEIF($range, $condition, $averageRange = [])
{
< $returnValue = 0;
<
< $aArgs = Functions::flattenArray($aArgs);
< $averageArgs = Functions::flattenArray($averageArgs);
< if (empty($averageArgs)) {
< $averageArgs = $aArgs;
< }
< $condition = Functions::ifCondition($condition);
< $conditionIsNumeric = strpos($condition, '"') === false;
<
< // Loop through arguments
< $aCount = 0;
< foreach ($aArgs as $key => $arg) {
< if (!is_numeric($arg)) {
< if ($conditionIsNumeric) {
< continue;
< }
< $arg = Calculation::wrapResult(strtoupper($arg));
< } elseif (!$conditionIsNumeric) {
< continue;
< }
< $testCondition = '=' . $arg . $condition;
< if (Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
< $returnValue += $averageArgs[$key];
< ++$aCount;
< }
< }
<
< if ($aCount > 0) {
< return $returnValue / $aCount;
< }
<
< return Functions::DIV0();
> return Conditional::AVERAGEIF($range, $condition, $averageRange);
}
/**
* BETADIST.
*
* Returns the beta distribution.
*
> * @Deprecated 1.18.0
* @param float $value Value at which you want to evaluate the distribution
> *
* @param float $alpha Parameter to the distribution
> * @see Statistical\Distributions\Beta::distribution()
* @param float $beta Parameter to the distribution
> * Use the distribution() method in the Statistical\Distributions\Beta class instead
* @param mixed $rMin
> *
* @param mixed $rMax
*
< * @return float|string
> * @return array|float|string
*/
public static function BETADIST($value, $alpha, $beta, $rMin = 0, $rMax = 1)
{
< $value = Functions::flattenSingleValue($value);
< $alpha = Functions::flattenSingleValue($alpha);
< $beta = Functions::flattenSingleValue($beta);
< $rMin = Functions::flattenSingleValue($rMin);
< $rMax = Functions::flattenSingleValue($rMax);
<
< if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) {
< if (($value < $rMin) || ($value > $rMax) || ($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax)) {
< return Functions::NAN();
< }
< if ($rMin > $rMax) {
< $tmp = $rMin;
< $rMin = $rMax;
< $rMax = $tmp;
< }
< $value -= $rMin;
< $value /= ($rMax - $rMin);
<
< return self::incompleteBeta($value, $alpha, $beta);
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\Beta::distribution($value, $alpha, $beta, $rMin, $rMax);
}
/**
* BETAINV.
*
* Returns the inverse of the Beta distribution.
*
> * @Deprecated 1.18.0
* @param float $probability Probability at which you want to evaluate the distribution
> *
* @param float $alpha Parameter to the distribution
> * @see Statistical\Distributions\Beta::inverse()
* @param float $beta Parameter to the distribution
> * Use the inverse() method in the Statistical\Distributions\Beta class instead
* @param float $rMin Minimum value
> *
* @param float $rMax Maximum value
*
< * @return float|string
> * @return array|float|string
*/
public static function BETAINV($probability, $alpha, $beta, $rMin = 0, $rMax = 1)
{
< $probability = Functions::flattenSingleValue($probability);
< $alpha = Functions::flattenSingleValue($alpha);
< $beta = Functions::flattenSingleValue($beta);
< $rMin = Functions::flattenSingleValue($rMin);
< $rMax = Functions::flattenSingleValue($rMax);
<
< if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) {
< if (($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax) || ($probability <= 0) || ($probability > 1)) {
< return Functions::NAN();
< }
< if ($rMin > $rMax) {
< $tmp = $rMin;
< $rMin = $rMax;
< $rMax = $tmp;
< }
< $a = 0;
< $b = 2;
<
< $i = 0;
< while ((($b - $a) > Functions::PRECISION) && ($i++ < self::MAX_ITERATIONS)) {
< $guess = ($a + $b) / 2;
< $result = self::BETADIST($guess, $alpha, $beta);
< if (($result == $probability) || ($result == 0)) {
< $b = $a;
< } elseif ($result > $probability) {
< $b = $guess;
< } else {
< $a = $guess;
< }
< }
< if ($i == self::MAX_ITERATIONS) {
< return Functions::NA();
< }
<
< return round($rMin + $guess * ($rMax - $rMin), 12);
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\Beta::inverse($probability, $alpha, $beta, $rMin, $rMax);
}
/**
* BINOMDIST.
*
* Returns the individual term binomial distribution probability. Use BINOMDIST in problems with
* a fixed number of tests or trials, when the outcomes of any trial are only success or failure,
* when trials are independent, and when the probability of success is constant throughout the
* experiment. For example, BINOMDIST can calculate the probability that two of the next three
* babies born are male.
*
< * @param float $value Number of successes in trials
< * @param float $trials Number of trials
< * @param float $probability Probability of success on each trial
< * @param bool $cumulative
> * @Deprecated 1.18.0
*
< * @return float|string
> * @see Statistical\Distributions\Binomial::distribution()
> * Use the distribution() method in the Statistical\Distributions\Binomial class instead
> *
> * @param mixed $value Number of successes in trials
> * @param mixed $trials Number of trials
> * @param mixed $probability Probability of success on each trial
> * @param mixed $cumulative
> *
> * @return array|float|string
*/
public static function BINOMDIST($value, $trials, $probability, $cumulative)
{
< $value = Functions::flattenSingleValue($value);
< $trials = Functions::flattenSingleValue($trials);
< $probability = Functions::flattenSingleValue($probability);
<
< if ((is_numeric($value)) && (is_numeric($trials)) && (is_numeric($probability))) {
< $value = floor($value);
< $trials = floor($trials);
< if (($value < 0) || ($value > $trials)) {
< return Functions::NAN();
< }
< if (($probability < 0) || ($probability > 1)) {
< return Functions::NAN();
< }
< if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
< if ($cumulative) {
< $summer = 0;
< for ($i = 0; $i <= $value; ++$i) {
< $summer += MathTrig::COMBIN($trials, $i) * $probability ** $i * (1 - $probability) ** ($trials - $i);
< }
<
< return $summer;
< }
<
< return MathTrig::COMBIN($trials, $value) * $probability ** $value * (1 - $probability) ** ($trials - $value);
< }
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\Binomial::distribution($value, $trials, $probability, $cumulative);
}
/**
* CHIDIST.
*
* Returns the one-tailed probability of the chi-squared distribution.
*
> * @Deprecated 1.18.0
* @param float $value Value for the function
> *
* @param float $degrees degrees of freedom
> * @see Statistical\Distributions\ChiSquared::distributionRightTail()
*
> * Use the distributionRightTail() method in the Statistical\Distributions\ChiSquared class instead
* @return float|string
> *
< * @return float|string
> * @return array|float|string
public static function CHIDIST($value, $degrees)
{
< $value = Functions::flattenSingleValue($value);
< $degrees = Functions::flattenSingleValue($degrees);
<
< if ((is_numeric($value)) && (is_numeric($degrees))) {
< $degrees = floor($degrees);
< if ($degrees < 1) {
< return Functions::NAN();
< }
< if ($value < 0) {
< if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
< return 1;
< }
<
< return Functions::NAN();
< }
<
< return 1 - (self::incompleteGamma($degrees / 2, $value / 2) / self::gamma($degrees / 2));
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\ChiSquared::distributionRightTail($value, $degrees);
}
/**
* CHIINV.
*
* Returns the one-tailed probability of the chi-squared distribution.
*
> * @Deprecated 1.18.0
* @param float $probability Probability for the function
> *
* @param float $degrees degrees of freedom
> * @see Statistical\Distributions\ChiSquared::inverseRightTail()
*
> * Use the inverseRightTail() method in the Statistical\Distributions\ChiSquared class instead
* @return float|string
> *
< * @return float|string
> * @return array|float|string
public static function CHIINV($probability, $degrees)
{
< $probability = Functions::flattenSingleValue($probability);
< $degrees = Functions::flattenSingleValue($degrees);
<
< if ((is_numeric($probability)) && (is_numeric($degrees))) {
< $degrees = floor($degrees);
<
< $xLo = 100;
< $xHi = 0;
<
< $x = $xNew = 1;
< $dx = 1;
< $i = 0;
<
< while ((abs($dx) > Functions::PRECISION) && ($i++ < self::MAX_ITERATIONS)) {
< // Apply Newton-Raphson step
< $result = 1 - (self::incompleteGamma($degrees / 2, $x / 2) / self::gamma($degrees / 2));
< $error = $result - $probability;
< if ($error == 0.0) {
< $dx = 0;
< } elseif ($error < 0.0) {
< $xLo = $x;
< } else {
< $xHi = $x;
< }
< // Avoid division by zero
< if ($result != 0.0) {
< $dx = $error / $result;
< $xNew = $x - $dx;
< }
< // If the NR fails to converge (which for example may be the
< // case if the initial guess is too rough) we apply a bisection
< // step to determine a more narrow interval around the root.
< if (($xNew < $xLo) || ($xNew > $xHi) || ($result == 0.0)) {
< $xNew = ($xLo + $xHi) / 2;
< $dx = $xNew - $x;
< }
< $x = $xNew;
< }
< if ($i == self::MAX_ITERATIONS) {
< return Functions::NA();
< }
<
< return round($x, 12);
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\ChiSquared::inverseRightTail($probability, $degrees);
}
/**
* CONFIDENCE.
*
* Returns the confidence interval for a population mean
*
> * @Deprecated 1.18.0
* @param float $alpha
> *
* @param float $stdDev Standard Deviation
> * @see Statistical\Confidence::CONFIDENCE()
* @param float $size
> * Use the CONFIDENCE() method in the Statistical\Confidence class instead
*
> *
< * @return float|string
> * @return array|float|string
*/
public static function CONFIDENCE($alpha, $stdDev, $size)
{
< $alpha = Functions::flattenSingleValue($alpha);
< $stdDev = Functions::flattenSingleValue($stdDev);
< $size = Functions::flattenSingleValue($size);
<
< if ((is_numeric($alpha)) && (is_numeric($stdDev)) && (is_numeric($size))) {
< $size = floor($size);
< if (($alpha <= 0) || ($alpha >= 1)) {
< return Functions::NAN();
< }
< if (($stdDev <= 0) || ($size < 1)) {
< return Functions::NAN();
< }
<
< return self::NORMSINV(1 - $alpha / 2) * $stdDev / sqrt($size);
< }
<
< return Functions::VALUE();
> return Confidence::CONFIDENCE($alpha, $stdDev, $size);
}
/**
* CORREL.
*
* Returns covariance, the average of the products of deviations for each data point pair.
*
> * @Deprecated 1.18.0
* @param mixed $yValues array of mixed Data Series Y
> *
* @param null|mixed $xValues array of mixed Data Series X
> * @see Statistical\Trends::CORREL()
*
> * Use the CORREL() method in the Statistical\Trends class instead
* @return float|string
> *
*/
public static function CORREL($yValues, $xValues = null)
{
< if (($xValues === null) || (!is_array($yValues)) || (!is_array($xValues))) {
< return Functions::VALUE();
< }
< if (!self::checkTrendArrays($yValues, $xValues)) {
< return Functions::VALUE();
< }
< $yValueCount = count($yValues);
< $xValueCount = count($xValues);
<
< if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
< return Functions::NA();
< } elseif ($yValueCount == 1) {
< return Functions::DIV0();
< }
<
< $bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
<
< return $bestFitLinear->getCorrelation();
> return Trends::CORREL($xValues, $yValues);
}
/**
* COUNT.
*
* Counts the number of cells that contain numbers within the list of arguments
*
* Excel Function:
* COUNT(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\Counts::COUNT()
* @return int
> * Use the COUNT() method in the Statistical\Counts class instead
*/
> *
public static function COUNT(...$args)
{
< $returnValue = 0;
<
< // Loop through arguments
< $aArgs = Functions::flattenArrayIndexed($args);
< foreach ($aArgs as $k => $arg) {
< $arg = self::testAcceptedBoolean($arg, $k);
< // Is it a numeric value?
< // Strings containing numeric values are only counted if they are string literals (not cell values)
< // and then only in MS Excel and in Open Office, not in Gnumeric
< if (self::isAcceptedCountable($arg, $k)) {
< ++$returnValue;
< }
< }
<
< return $returnValue;
> return Counts::COUNT(...$args);
}
/**
* COUNTA.
*
* Counts the number of cells that are not empty within the list of arguments
*
* Excel Function:
* COUNTA(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\Counts::COUNTA()
* @return int
> * Use the COUNTA() method in the Statistical\Counts class instead
*/
> *
public static function COUNTA(...$args)
{
< $returnValue = 0;
<
< // Loop through arguments
< $aArgs = Functions::flattenArrayIndexed($args);
< foreach ($aArgs as $k => $arg) {
< // Nulls are counted if literals, but not if cell values
< if ($arg !== null || (!Functions::isCellValue($k))) {
< ++$returnValue;
< }
< }
<
< return $returnValue;
> return Counts::COUNTA(...$args);
}
/**
* COUNTBLANK.
*
* Counts the number of empty cells within the list of arguments
*
* Excel Function:
* COUNTBLANK(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\Counts::COUNTBLANK()
* @return int
> * Use the COUNTBLANK() method in the Statistical\Counts class instead
*/
> *
public static function COUNTBLANK(...$args)
{
< $returnValue = 0;
<
< // Loop through arguments
< $aArgs = Functions::flattenArray($args);
< foreach ($aArgs as $arg) {
< // Is it a blank cell?
< if (($arg === null) || ((is_string($arg)) && ($arg == ''))) {
< ++$returnValue;
< }
< }
<
< return $returnValue;
> return Counts::COUNTBLANK(...$args);
}
/**
* COUNTIF.
*
* Counts the number of cells that contain numbers within the list of arguments
*
* Excel Function:
< * COUNTIF(value1[,value2[, ...]],condition)
> * COUNTIF(range,condition)
> *
> * @Deprecated 1.17.0
*
< * @param mixed $aArgs Data values
> * @see Statistical\Conditional::COUNTIF()
> * Use the COUNTIF() method in the Statistical\Conditional class instead
> *
> * @param mixed $range Data values
* @param string $condition the criteria that defines which cells will be counted
*
* @return int
*/
< public static function COUNTIF($aArgs, $condition)
> public static function COUNTIF($range, $condition)
{
< $returnValue = 0;
<
< $aArgs = Functions::flattenArray($aArgs);
< $condition = Functions::ifCondition($condition);
< $conditionIsNumeric = strpos($condition, '"') === false;
< // Loop through arguments
< foreach ($aArgs as $arg) {
< if (!is_numeric($arg)) {
< if ($conditionIsNumeric) {
< continue;
< }
< $arg = Calculation::wrapResult(strtoupper($arg));
< } elseif (!$conditionIsNumeric) {
< continue;
< }
< $testCondition = '=' . $arg . $condition;
< if (Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
< // Is it a value within our criteria
< ++$returnValue;
< }
< }
<
< return $returnValue;
> return Conditional::COUNTIF($range, $condition);
}
/**
* COUNTIFS.
*
* Counts the number of cells that contain numbers within the list of arguments
*
* Excel Function:
* COUNTIFS(criteria_range1, criteria1, [criteria_range2, criteria2]…)
*
< * @param mixed $args Criterias
> * @Deprecated 1.17.0
> *
> * @see Statistical\Conditional::COUNTIFS()
> * Use the COUNTIFS() method in the Statistical\Conditional class instead
> *
> * @param mixed $args Pairs of Ranges and Criteria
*
* @return int
*/
public static function COUNTIFS(...$args)
{
< $arrayList = $args;
<
< // Return value
< $returnValue = 0;
<
< if (empty($arrayList)) {
< return $returnValue;
< }
<
< $aArgsArray = [];
< $conditions = [];
<
< while (count($arrayList) > 0) {
< $aArgsArray[] = Functions::flattenArray(array_shift($arrayList));
< $conditions[] = Functions::ifCondition(array_shift($arrayList));
< }
<
< // Loop through each arg and see if arguments and conditions are true
< foreach (array_keys($aArgsArray[0]) as $index) {
< $valid = true;
<
< foreach ($conditions as $cidx => $condition) {
< $conditionIsNumeric = strpos($condition, '"') === false;
< $arg = $aArgsArray[$cidx][$index];
<
< // Loop through arguments
< if (!is_numeric($arg)) {
< if ($conditionIsNumeric) {
< $valid = false;
<
< break; // if false found, don't need to check other conditions
< }
< $arg = Calculation::wrapResult(strtoupper($arg));
< } elseif (!$conditionIsNumeric) {
< $valid = false;
<
< break; // if false found, don't need to check other conditions
< }
< $testCondition = '=' . $arg . $condition;
< if (!Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
< // Is not a value within our criteria
< $valid = false;
<
< break; // if false found, don't need to check other conditions
< }
< }
<
< if ($valid) {
< ++$returnValue;
< }
< }
<
< // Return
< return $returnValue;
> return Conditional::COUNTIFS(...$args);
}
/**
* COVAR.
*
* Returns covariance, the average of the products of deviations for each data point pair.
*
> * @Deprecated 1.18.0
* @param mixed $yValues array of mixed Data Series Y
> *
* @param mixed $xValues array of mixed Data Series X
> * @see Statistical\Trends::COVAR()
*
> * Use the COVAR() method in the Statistical\Trends class instead
* @return float|string
> *
*/
public static function COVAR($yValues, $xValues)
{
< if (!self::checkTrendArrays($yValues, $xValues)) {
< return Functions::VALUE();
< }
< $yValueCount = count($yValues);
< $xValueCount = count($xValues);
<
< if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
< return Functions::NA();
< } elseif ($yValueCount == 1) {
< return Functions::DIV0();
< }
<
< $bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
<
< return $bestFitLinear->getCovariance();
> return Trends::COVAR($yValues, $xValues);
}
/**
* CRITBINOM.
*
* Returns the smallest value for which the cumulative binomial distribution is greater
* than or equal to a criterion value
*
* See https://support.microsoft.com/en-us/help/828117/ for details of the algorithm used
*
> * @Deprecated 1.18.0
* @param float $trials number of Bernoulli trials
> *
* @param float $probability probability of a success on each trial
> * @see Statistical\Distributions\Binomial::inverse()
* @param float $alpha criterion value
> * Use the inverse() method in the Statistical\Distributions\Binomial class instead
*
> *
< * @return int|string
< *
< * @TODO Warning. This implementation differs from the algorithm detailed on the MS
< * web site in that $CumPGuessMinus1 = $CumPGuess - 1 rather than $CumPGuess - $PGuess
< * This eliminates a potential endless loop error, but may have an adverse affect on the
< * accuracy of the function (although all my tests have so far returned correct results).
> * @return array|int|string
*/
public static function CRITBINOM($trials, $probability, $alpha)
{
< $trials = floor(Functions::flattenSingleValue($trials));
< $probability = Functions::flattenSingleValue($probability);
< $alpha = Functions::flattenSingleValue($alpha);
<
< if ((is_numeric($trials)) && (is_numeric($probability)) && (is_numeric($alpha))) {
< $trials = (int) $trials;
< if ($trials < 0) {
< return Functions::NAN();
< } elseif (($probability < 0.0) || ($probability > 1.0)) {
< return Functions::NAN();
< } elseif (($alpha < 0.0) || ($alpha > 1.0)) {
< return Functions::NAN();
< }
<
< if ($alpha <= 0.5) {
< $t = sqrt(log(1 / ($alpha * $alpha)));
< $trialsApprox = 0 - ($t + (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t));
< } else {
< $t = sqrt(log(1 / (1 - $alpha) ** 2));
< $trialsApprox = $t - (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t);
< }
<
< $Guess = floor($trials * $probability + $trialsApprox * sqrt($trials * $probability * (1 - $probability)));
< if ($Guess < 0) {
< $Guess = 0;
< } elseif ($Guess > $trials) {
< $Guess = $trials;
< }
<
< $TotalUnscaledProbability = $UnscaledPGuess = $UnscaledCumPGuess = 0.0;
< $EssentiallyZero = 10e-12;
<
< $m = floor($trials * $probability);
< ++$TotalUnscaledProbability;
< if ($m == $Guess) {
< ++$UnscaledPGuess;
< }
< if ($m <= $Guess) {
< ++$UnscaledCumPGuess;
< }
<
< $PreviousValue = 1;
< $Done = false;
< $k = $m + 1;
< while ((!$Done) && ($k <= $trials)) {
< $CurrentValue = $PreviousValue * ($trials - $k + 1) * $probability / ($k * (1 - $probability));
< $TotalUnscaledProbability += $CurrentValue;
< if ($k == $Guess) {
< $UnscaledPGuess += $CurrentValue;
< }
< if ($k <= $Guess) {
< $UnscaledCumPGuess += $CurrentValue;
< }
< if ($CurrentValue <= $EssentiallyZero) {
< $Done = true;
< }
< $PreviousValue = $CurrentValue;
< ++$k;
< }
<
< $PreviousValue = 1;
< $Done = false;
< $k = $m - 1;
< while ((!$Done) && ($k >= 0)) {
< $CurrentValue = $PreviousValue * $k + 1 * (1 - $probability) / (($trials - $k) * $probability);
< $TotalUnscaledProbability += $CurrentValue;
< if ($k == $Guess) {
< $UnscaledPGuess += $CurrentValue;
< }
< if ($k <= $Guess) {
< $UnscaledCumPGuess += $CurrentValue;
< }
< if ($CurrentValue <= $EssentiallyZero) {
< $Done = true;
< }
< $PreviousValue = $CurrentValue;
< --$k;
< }
<
< $PGuess = $UnscaledPGuess / $TotalUnscaledProbability;
< $CumPGuess = $UnscaledCumPGuess / $TotalUnscaledProbability;
<
< $CumPGuessMinus1 = $CumPGuess - 1;
<
< while (true) {
< if (($CumPGuessMinus1 < $alpha) && ($CumPGuess >= $alpha)) {
< return $Guess;
< } elseif (($CumPGuessMinus1 < $alpha) && ($CumPGuess < $alpha)) {
< $PGuessPlus1 = $PGuess * ($trials - $Guess) * $probability / $Guess / (1 - $probability);
< $CumPGuessMinus1 = $CumPGuess;
< $CumPGuess = $CumPGuess + $PGuessPlus1;
< $PGuess = $PGuessPlus1;
< ++$Guess;
< } elseif (($CumPGuessMinus1 >= $alpha) && ($CumPGuess >= $alpha)) {
< $PGuessMinus1 = $PGuess * $Guess * (1 - $probability) / ($trials - $Guess + 1) / $probability;
< $CumPGuess = $CumPGuessMinus1;
< $CumPGuessMinus1 = $CumPGuessMinus1 - $PGuess;
< $PGuess = $PGuessMinus1;
< --$Guess;
< }
< }
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\Binomial::inverse($trials, $probability, $alpha);
}
/**
* DEVSQ.
*
* Returns the sum of squares of deviations of data points from their sample mean.
*
* Excel Function:
* DEVSQ(value1[,value2[, ...]])
*
> * @Deprecated 1.18.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\Deviations::sumSquares()
* @return float|string
> * Use the sumSquares() method in the Statistical\Deviations class instead
*/
> *
public static function DEVSQ(...$args)
{
< $aArgs = Functions::flattenArrayIndexed($args);
<
< // Return value
< $returnValue = null;
<
< $aMean = self::AVERAGE($aArgs);
< if ($aMean != Functions::DIV0()) {
< $aCount = -1;
< foreach ($aArgs as $k => $arg) {
< // Is it a numeric value?
< if (
< (is_bool($arg)) &&
< ((!Functions::isCellValue($k)) ||
< (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))
< ) {
< $arg = (int) $arg;
< }
< if ((is_numeric($arg)) && (!is_string($arg))) {
< if ($returnValue === null) {
< $returnValue = ($arg - $aMean) ** 2;
< } else {
< $returnValue += ($arg - $aMean) ** 2;
< }
< ++$aCount;
< }
< }
<
< // Return
< if ($returnValue === null) {
< return Functions::NAN();
< }
<
< return $returnValue;
< }
<
< return Functions::NA();
> return Statistical\Deviations::sumSquares(...$args);
}
/**
* EXPONDIST.
*
* Returns the exponential distribution. Use EXPONDIST to model the time between events,
* such as how long an automated bank teller takes to deliver cash. For example, you can
* use EXPONDIST to determine the probability that the process takes at most 1 minute.
*
> * @Deprecated 1.18.0
* @param float $value Value of the function
> *
* @param float $lambda The parameter value
> * @see Statistical\Distributions\Exponential::distribution()
* @param bool $cumulative
> * Use the distribution() method in the Statistical\Distributions\Exponential class instead
*
> *
< * @return float|string
> * @return array|float|string
*/
public static function EXPONDIST($value, $lambda, $cumulative)
{
< $value = Functions::flattenSingleValue($value);
< $lambda = Functions::flattenSingleValue($lambda);
< $cumulative = Functions::flattenSingleValue($cumulative);
<
< if ((is_numeric($value)) && (is_numeric($lambda))) {
< if (($value < 0) || ($lambda < 0)) {
< return Functions::NAN();
< }
< if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
< if ($cumulative) {
< return 1 - exp(0 - $value * $lambda);
< }
<
< return $lambda * exp(0 - $value * $lambda);
< }
< }
<
< return Functions::VALUE();
< }
<
< private static function betaFunction($a, $b)
< {
< return (self::gamma($a) * self::gamma($b)) / self::gamma($a + $b);
< }
<
< private static function regularizedIncompleteBeta($value, $a, $b)
< {
< return self::incompleteBeta($value, $a, $b) / self::betaFunction($a, $b);
> return Statistical\Distributions\Exponential::distribution($value, $lambda, $cumulative);
}
/**
* F.DIST.
*
* Returns the F probability distribution.
* You can use this function to determine whether two data sets have different degrees of diversity.
* For example, you can examine the test scores of men and women entering high school, and determine
* if the variability in the females is different from that found in the males.
*
> * @Deprecated 1.18.0
* @param float $value Value of the function
> *
* @param int $u The numerator degrees of freedom
> * @see Statistical\Distributions\F::distribution()
* @param int $v The denominator degrees of freedom
> * Use the distribution() method in the Statistical\Distributions\Exponential class instead
* @param bool $cumulative If cumulative is TRUE, F.DIST returns the cumulative distribution function;
> *
* if FALSE, it returns the probability density function.
*
< * @return float|string
> * @return array|float|string
*/
public static function FDIST2($value, $u, $v, $cumulative)
{
< $value = Functions::flattenSingleValue($value);
< $u = Functions::flattenSingleValue($u);
< $v = Functions::flattenSingleValue($v);
< $cumulative = Functions::flattenSingleValue($cumulative);
<
< if (is_numeric($value) && is_numeric($u) && is_numeric($v)) {
< if ($value < 0 || $u < 1 || $v < 1) {
< return Functions::NAN();
< }
<
< $cumulative = (bool) $cumulative;
< $u = (int) $u;
< $v = (int) $v;
<
< if ($cumulative) {
< $adjustedValue = ($u * $value) / ($u * $value + $v);
<
< return self::incompleteBeta($adjustedValue, $u / 2, $v / 2);
< }
<
< return (self::gamma(($v + $u) / 2) / (self::gamma($u / 2) * self::gamma($v / 2))) *
< (($u / $v) ** ($u / 2)) *
< (($value ** (($u - 2) / 2)) / ((1 + ($u / $v) * $value) ** (($u + $v) / 2)));
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\F::distribution($value, $u, $v, $cumulative);
}
/**
* FISHER.
*
* Returns the Fisher transformation at x. This transformation produces a function that
* is normally distributed rather than skewed. Use this function to perform hypothesis
* testing on the correlation coefficient.
*
> * @Deprecated 1.18.0
* @param float $value
> *
*
> * @see Statistical\Distributions\Fisher::distribution()
* @return float|string
> * Use the distribution() method in the Statistical\Distributions\Fisher class instead
*/
> *
< * @return float|string
> * @return array|float|string
{
< $value = Functions::flattenSingleValue($value);
<
< if (is_numeric($value)) {
< if (($value <= -1) || ($value >= 1)) {
< return Functions::NAN();
< }
<
< return 0.5 * log((1 + $value) / (1 - $value));
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\Fisher::distribution($value);
}
/**
* FISHERINV.
*
* Returns the inverse of the Fisher transformation. Use this transformation when
* analyzing correlations between ranges or arrays of data. If y = FISHER(x), then
* FISHERINV(y) = x.
*
> * @Deprecated 1.18.0
* @param float $value
> *
*
> * @see Statistical\Distributions\Fisher::inverse()
* @return float|string
> * Use the inverse() method in the Statistical\Distributions\Fisher class instead
*/
> *
< * @return float|string
> * @return array|float|string
{
< $value = Functions::flattenSingleValue($value);
<
< if (is_numeric($value)) {
< return (exp(2 * $value) - 1) / (exp(2 * $value) + 1);
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\Fisher::inverse($value);
}
/**
* FORECAST.
*
* Calculates, or predicts, a future value by using existing values. The predicted value is a y-value for a given x-value.
*
> * @Deprecated 1.18.0
* @param float $xValue Value of X for which we want to find Y
> *
* @param mixed $yValues array of mixed Data Series Y
> * @see Statistical\Trends::FORECAST()
* @param mixed $xValues of mixed Data Series X
> * Use the FORECAST() method in the Statistical\Trends class instead
*
> *
< * @return bool|float|string
> * @return array|bool|float|string
*/
public static function FORECAST($xValue, $yValues, $xValues)
{
< $xValue = Functions::flattenSingleValue($xValue);
< if (!is_numeric($xValue)) {
< return Functions::VALUE();
< } elseif (!self::checkTrendArrays($yValues, $xValues)) {
< return Functions::VALUE();
< }
< $yValueCount = count($yValues);
< $xValueCount = count($xValues);
<
< if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
< return Functions::NA();
< } elseif ($yValueCount == 1) {
< return Functions::DIV0();
< }
<
< $bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
<
< return $bestFitLinear->getValueOfYForX($xValue);
> return Trends::FORECAST($xValue, $yValues, $xValues);
}
/**
* GAMMA.
*
< * Return the gamma function value.
> * Returns the gamma function value.
> *
> * @Deprecated 1.18.0
> *
> * @see Statistical\Distributions\Gamma::gamma()
> * Use the gamma() method in the Statistical\Distributions\Gamma class instead
*
* @param float $value
*
< * @return float|string The result, or a string containing an error
> * @return array|float|string The result, or a string containing an error
*/
public static function GAMMAFunction($value)
{
< $value = Functions::flattenSingleValue($value);
< if (!is_numeric($value)) {
< return Functions::VALUE();
< } elseif ((((int) $value) == ((float) $value)) && $value <= 0.0) {
< return Functions::NAN();
< }
<
< return self::gamma($value);
> return Statistical\Distributions\Gamma::gamma($value);
}
/**
* GAMMADIST.
*
* Returns the gamma distribution.
*
> * @Deprecated 1.18.0
* @param float $value Value at which you want to evaluate the distribution
> *
* @param float $a Parameter to the distribution
> * @see Statistical\Distributions\Gamma::distribution()
* @param float $b Parameter to the distribution
> * Use the distribution() method in the Statistical\Distributions\Gamma class instead
* @param bool $cumulative
> *
*
< * @return float|string
> * @return array|float|string
*/
public static function GAMMADIST($value, $a, $b, $cumulative)
{
< $value = Functions::flattenSingleValue($value);
< $a = Functions::flattenSingleValue($a);
< $b = Functions::flattenSingleValue($b);
<
< if ((is_numeric($value)) && (is_numeric($a)) && (is_numeric($b))) {
< if (($value < 0) || ($a <= 0) || ($b <= 0)) {
< return Functions::NAN();
< }
< if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
< if ($cumulative) {
< return self::incompleteGamma($a, $value / $b) / self::gamma($a);
< }
<
< return (1 / ($b ** $a * self::gamma($a))) * $value ** ($a - 1) * exp(0 - ($value / $b));
< }
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\Gamma::distribution($value, $a, $b, $cumulative);
}
/**
* GAMMAINV.
*
* Returns the inverse of the Gamma distribution.
*
> * @Deprecated 1.18.0
* @param float $probability Probability at which you want to evaluate the distribution
> *
* @param float $alpha Parameter to the distribution
> * @see Statistical\Distributions\Gamma::inverse()
* @param float $beta Parameter to the distribution
> * Use the inverse() method in the Statistical\Distributions\Gamma class instead
*
> *
< * @return float|string
> * @return array|float|string
*/
public static function GAMMAINV($probability, $alpha, $beta)
{
< $probability = Functions::flattenSingleValue($probability);
< $alpha = Functions::flattenSingleValue($alpha);
< $beta = Functions::flattenSingleValue($beta);
<
< if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta))) {
< if (($alpha <= 0) || ($beta <= 0) || ($probability < 0) || ($probability > 1)) {
< return Functions::NAN();
< }
<
< $xLo = 0;
< $xHi = $alpha * $beta * 5;
<
< $x = $xNew = 1;
< $dx = 1024;
< $i = 0;
<
< while ((abs($dx) > Functions::PRECISION) && ($i++ < self::MAX_ITERATIONS)) {
< // Apply Newton-Raphson step
< $error = self::GAMMADIST($x, $alpha, $beta, true) - $probability;
< if ($error < 0.0) {
< $xLo = $x;
< } else {
< $xHi = $x;
< }
< $pdf = self::GAMMADIST($x, $alpha, $beta, false);
< // Avoid division by zero
< if ($pdf != 0.0) {
< $dx = $error / $pdf;
< $xNew = $x - $dx;
< }
< // If the NR fails to converge (which for example may be the
< // case if the initial guess is too rough) we apply a bisection
< // step to determine a more narrow interval around the root.
< if (($xNew < $xLo) || ($xNew > $xHi) || ($pdf == 0.0)) {
< $xNew = ($xLo + $xHi) / 2;
< $dx = $xNew - $x;
< }
< $x = $xNew;
< }
< if ($i == self::MAX_ITERATIONS) {
< return Functions::NA();
< }
<
< return $x;
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\Gamma::inverse($probability, $alpha, $beta);
}
/**
* GAMMALN.
*
* Returns the natural logarithm of the gamma function.
*
> * @Deprecated 1.18.0
* @param float $value
> *
*
> * @see Statistical\Distributions\Gamma::ln()
* @return float|string
> * Use the ln() method in the Statistical\Distributions\Gamma class instead
*/
> *
< * @return float|string
> * @return array|float|string
{
< $value = Functions::flattenSingleValue($value);
<
< if (is_numeric($value)) {
< if ($value <= 0) {
< return Functions::NAN();
< }
<
< return log(self::gamma($value));
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\Gamma::ln($value);
}
/**
* GAUSS.
*
* Calculates the probability that a member of a standard normal population will fall between
* the mean and z standard deviations from the mean.
*
> * @Deprecated 1.18.0
* @param float $value
> *
*
> * @see Statistical\Distributions\StandardNormal::gauss()
* @return float|string The result, or a string containing an error
> * Use the gauss() method in the Statistical\Distributions\StandardNormal class instead
*/
> *
< * @return float|string The result, or a string containing an error
> * @return array|float|string The result, or a string containing an error
{
< $value = Functions::flattenSingleValue($value);
< if (!is_numeric($value)) {
< return Functions::VALUE();
< }
<
< return self::NORMDIST($value, 0, 1, true) - 0.5;
> return Statistical\Distributions\StandardNormal::gauss($value);
}
/**
* GEOMEAN.
*
* Returns the geometric mean of an array or range of positive data. For example, you
* can use GEOMEAN to calculate average growth rate given compound interest with
* variable rates.
*
* Excel Function:
* GEOMEAN(value1[,value2[, ...]])
*
> * @Deprecated 1.18.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\Averages\Mean::geometric()
* @return float|string
> * Use the geometric() method in the Statistical\Averages\Mean class instead
*/
> *
public static function GEOMEAN(...$args)
{
< $aArgs = Functions::flattenArray($args);
<
< $aMean = MathTrig::PRODUCT($aArgs);
< if (is_numeric($aMean) && ($aMean > 0)) {
< $aCount = self::COUNT($aArgs);
< if (self::MIN($aArgs) > 0) {
< return $aMean ** (1 / $aCount);
< }
< }
<
< return Functions::NAN();
> return Statistical\Averages\Mean::geometric(...$args);
}
/**
* GROWTH.
*
* Returns values along a predicted exponential Trend
*
> * @Deprecated 1.18.0
* @param mixed[] $yValues Data Series Y
> *
* @param mixed[] $xValues Data Series X
> * @see Statistical\Trends::GROWTH()
* @param mixed[] $newValues Values of X for which we want to find Y
> * Use the GROWTH() method in the Statistical\Trends class instead
* @param bool $const a logical value specifying whether to force the intersect to equal 0
> *
*
< * @return array of float
> * @return float[]
*/
public static function GROWTH($yValues, $xValues = [], $newValues = [], $const = true)
{
< $yValues = Functions::flattenArray($yValues);
< $xValues = Functions::flattenArray($xValues);
< $newValues = Functions::flattenArray($newValues);
< $const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const);
<
< $bestFitExponential = Trend::calculate(Trend::TREND_EXPONENTIAL, $yValues, $xValues, $const);
< if (empty($newValues)) {
< $newValues = $bestFitExponential->getXValues();
< }
<
< $returnArray = [];
< foreach ($newValues as $xValue) {
< $returnArray[0][] = $bestFitExponential->getValueOfYForX($xValue);
< }
<
< return $returnArray;
> return Trends::GROWTH($yValues, $xValues, $newValues, $const);
}
/**
* HARMEAN.
*
* Returns the harmonic mean of a data set. The harmonic mean is the reciprocal of the
* arithmetic mean of reciprocals.
*
* Excel Function:
* HARMEAN(value1[,value2[, ...]])
*
> * @Deprecated 1.18.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\Averages\Mean::harmonic()
* @return float|string
> * Use the harmonic() method in the Statistical\Averages\Mean class instead
*/
> *
public static function HARMEAN(...$args)
{
< // Return value
< $returnValue = 0;
<
< // Loop through arguments
< $aArgs = Functions::flattenArray($args);
< if (self::MIN($aArgs) < 0) {
< return Functions::NAN();
< }
< $aCount = 0;
< foreach ($aArgs as $arg) {
< // Is it a numeric value?
< if ((is_numeric($arg)) && (!is_string($arg))) {
< if ($arg <= 0) {
< return Functions::NAN();
< }
< $returnValue += (1 / $arg);
< ++$aCount;
< }
< }
<
< // Return
< if ($aCount > 0) {
< return 1 / ($returnValue / $aCount);
< }
<
< return Functions::NA();
> return Statistical\Averages\Mean::harmonic(...$args);
}
/**
* HYPGEOMDIST.
*
* Returns the hypergeometric distribution. HYPGEOMDIST returns the probability of a given number of
* sample successes, given the sample size, population successes, and population size.
*
< * @param float $sampleSuccesses Number of successes in the sample
< * @param float $sampleNumber Size of the sample
< * @param float $populationSuccesses Number of successes in the population
< * @param float $populationNumber Population size
> * @Deprecated 1.18.0
*
< * @return float|string
> * @see Statistical\Distributions\HyperGeometric::distribution()
> * Use the distribution() method in the Statistical\Distributions\HyperGeometric class instead
> *
> * @param mixed $sampleSuccesses Number of successes in the sample
> * @param mixed $sampleNumber Size of the sample
> * @param mixed $populationSuccesses Number of successes in the population
> * @param mixed $populationNumber Population size
> *
> * @return array|float|string
*/
public static function HYPGEOMDIST($sampleSuccesses, $sampleNumber, $populationSuccesses, $populationNumber)
{
< $sampleSuccesses = Functions::flattenSingleValue($sampleSuccesses);
< $sampleNumber = Functions::flattenSingleValue($sampleNumber);
< $populationSuccesses = Functions::flattenSingleValue($populationSuccesses);
< $populationNumber = Functions::flattenSingleValue($populationNumber);
<
< if ((is_numeric($sampleSuccesses)) && (is_numeric($sampleNumber)) && (is_numeric($populationSuccesses)) && (is_numeric($populationNumber))) {
< $sampleSuccesses = floor($sampleSuccesses);
< $sampleNumber = floor($sampleNumber);
< $populationSuccesses = floor($populationSuccesses);
< $populationNumber = floor($populationNumber);
<
< if (($sampleSuccesses < 0) || ($sampleSuccesses > $sampleNumber) || ($sampleSuccesses > $populationSuccesses)) {
< return Functions::NAN();
< }
< if (($sampleNumber <= 0) || ($sampleNumber > $populationNumber)) {
< return Functions::NAN();
< }
< if (($populationSuccesses <= 0) || ($populationSuccesses > $populationNumber)) {
< return Functions::NAN();
< }
<
< return MathTrig::COMBIN($populationSuccesses, $sampleSuccesses) *
< MathTrig::COMBIN($populationNumber - $populationSuccesses, $sampleNumber - $sampleSuccesses) /
< MathTrig::COMBIN($populationNumber, $sampleNumber);
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\HyperGeometric::distribution(
> $sampleSuccesses,
> $sampleNumber,
> $populationSuccesses,
> $populationNumber
> );
}
/**
* INTERCEPT.
*
* Calculates the point at which a line will intersect the y-axis by using existing x-values and y-values.
*
> * @Deprecated 1.18.0
* @param mixed[] $yValues Data Series Y
> *
* @param mixed[] $xValues Data Series X
> * @see Statistical\Trends::INTERCEPT()
*
> * Use the INTERCEPT() method in the Statistical\Trends class instead
* @return float|string
> *
*/
public static function INTERCEPT($yValues, $xValues)
{
< if (!self::checkTrendArrays($yValues, $xValues)) {
< return Functions::VALUE();
< }
< $yValueCount = count($yValues);
< $xValueCount = count($xValues);
<
< if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
< return Functions::NA();
< } elseif ($yValueCount == 1) {
< return Functions::DIV0();
< }
<
< $bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
<
< return $bestFitLinear->getIntersect();
> return Trends::INTERCEPT($yValues, $xValues);
}
/**
* KURT.
*
* Returns the kurtosis of a data set. Kurtosis characterizes the relative peakedness
* or flatness of a distribution compared with the normal distribution. Positive
* kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a
* relatively flat distribution.
*
> * @Deprecated 1.18.0
* @param array ...$args Data Series
> *
*
> * @see Statistical\Deviations::kurtosis()
* @return float|string
> * Use the kurtosis() method in the Statistical\Deviations class instead
*/
> *
public static function KURT(...$args)
{
< $aArgs = Functions::flattenArrayIndexed($args);
< $mean = self::AVERAGE($aArgs);
< $stdDev = self::STDEV($aArgs);
<
< if ($stdDev > 0) {
< $count = $summer = 0;
< // Loop through arguments
< foreach ($aArgs as $k => $arg) {
< if (
< (is_bool($arg)) &&
< (!Functions::isMatrixValue($k))
< ) {
< } else {
< // Is it a numeric value?
< if ((is_numeric($arg)) && (!is_string($arg))) {
< $summer += (($arg - $mean) / $stdDev) ** 4;
< ++$count;
< }
< }
< }
<
< // Return
< if ($count > 3) {
< return $summer * ($count * ($count + 1) / (($count - 1) * ($count - 2) * ($count - 3))) - (3 * ($count - 1) ** 2 / (($count - 2) * ($count - 3)));
< }
< }
<
< return Functions::DIV0();
> return Statistical\Deviations::kurtosis(...$args);
}
/**
* LARGE.
*
* Returns the nth largest value in a data set. You can use this function to
* select a value based on its relative standing.
*
* Excel Function:
* LARGE(value1[,value2[, ...]],entry)
*
> * @Deprecated 1.18.0
* @param mixed $args Data values
> *
*
> * @see Statistical\Size::large()
* @return float|string The result, or a string containing an error
> * Use the large() method in the Statistical\Size class instead
*/
> *
public static function LARGE(...$args)
{
< $aArgs = Functions::flattenArray($args);
< $entry = array_pop($aArgs);
<
< if ((is_numeric($entry)) && (!is_string($entry))) {
< $entry = (int) floor($entry);
<
< // Calculate
< $mArgs = [];
< foreach ($aArgs as $arg) {
< // Is it a numeric value?
< if ((is_numeric($arg)) && (!is_string($arg))) {
< $mArgs[] = $arg;
< }
< }
< $count = self::COUNT($mArgs);
< --$entry;
< if (($entry < 0) || ($entry >= $count) || ($count == 0)) {
< return Functions::NAN();
< }
< rsort($mArgs);
<
< return $mArgs[$entry];
< }
<
< return Functions::VALUE();
> return Statistical\Size::large(...$args);
}
/**
* LINEST.
*
* Calculates the statistics for a line by using the "least squares" method to calculate a straight line that best fits your data,
* and then returns an array that describes the line.
*
> * @Deprecated 1.18.0
* @param mixed[] $yValues Data Series Y
> *
* @param null|mixed[] $xValues Data Series X
> * @see Statistical\Trends::LINEST()
* @param bool $const a logical value specifying whether to force the intersect to equal 0
> * Use the LINEST() method in the Statistical\Trends class instead
* @param bool $stats a logical value specifying whether to return additional regression statistics
> *
*
* @return array|int|string The result, or a string containing an error
*/
public static function LINEST($yValues, $xValues = null, $const = true, $stats = false)
{
< $const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const);
< $stats = ($stats === null) ? false : (bool) Functions::flattenSingleValue($stats);
< if ($xValues === null) {
< $xValues = range(1, count(Functions::flattenArray($yValues)));
< }
<
< if (!self::checkTrendArrays($yValues, $xValues)) {
< return Functions::VALUE();
< }
< $yValueCount = count($yValues);
< $xValueCount = count($xValues);
<
< if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
< return Functions::NA();
< } elseif ($yValueCount == 1) {
< return 0;
< }
<
< $bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues, $const);
< if ($stats) {
< return [
< [
< $bestFitLinear->getSlope(),
< $bestFitLinear->getSlopeSE(),
< $bestFitLinear->getGoodnessOfFit(),
< $bestFitLinear->getF(),
< $bestFitLinear->getSSRegression(),
< ],
< [
< $bestFitLinear->getIntersect(),
< $bestFitLinear->getIntersectSE(),
< $bestFitLinear->getStdevOfResiduals(),
< $bestFitLinear->getDFResiduals(),
< $bestFitLinear->getSSResiduals(),
< ],
< ];
< }
<
< return [
< $bestFitLinear->getSlope(),
< $bestFitLinear->getIntersect(),
< ];
> return Trends::LINEST($yValues, $xValues, $const, $stats);
}
/**
* LOGEST.
*
* Calculates an exponential curve that best fits the X and Y data series,
* and then returns an array that describes the line.
*
> * @Deprecated 1.18.0
* @param mixed[] $yValues Data Series Y
> *
* @param null|mixed[] $xValues Data Series X
> * @see Statistical\Trends::LOGEST()
* @param bool $const a logical value specifying whether to force the intersect to equal 0
> * Use the LOGEST() method in the Statistical\Trends class instead
* @param bool $stats a logical value specifying whether to return additional regression statistics
> *
*
* @return array|int|string The result, or a string containing an error
*/
public static function LOGEST($yValues, $xValues = null, $const = true, $stats = false)
{
< $const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const);
< $stats = ($stats === null) ? false : (bool) Functions::flattenSingleValue($stats);
< if ($xValues === null) {
< $xValues = range(1, count(Functions::flattenArray($yValues)));
< }
<
< if (!self::checkTrendArrays($yValues, $xValues)) {
< return Functions::VALUE();
< }
< $yValueCount = count($yValues);
< $xValueCount = count($xValues);
<
< foreach ($yValues as $value) {
< if ($value <= 0.0) {
< return Functions::NAN();
< }
< }
<
< if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
< return Functions::NA();
< } elseif ($yValueCount == 1) {
< return 1;
< }
<
< $bestFitExponential = Trend::calculate(Trend::TREND_EXPONENTIAL, $yValues, $xValues, $const);
< if ($stats) {
< return [
< [
< $bestFitExponential->getSlope(),
< $bestFitExponential->getSlopeSE(),
< $bestFitExponential->getGoodnessOfFit(),
< $bestFitExponential->getF(),
< $bestFitExponential->getSSRegression(),
< ],
< [
< $bestFitExponential->getIntersect(),
< $bestFitExponential->getIntersectSE(),
< $bestFitExponential->getStdevOfResiduals(),
< $bestFitExponential->getDFResiduals(),
< $bestFitExponential->getSSResiduals(),
< ],
< ];
< }
<
< return [
< $bestFitExponential->getSlope(),
< $bestFitExponential->getIntersect(),
< ];
> return Trends::LOGEST($yValues, $xValues, $const, $stats);
}
/**
* LOGINV.
*
* Returns the inverse of the normal cumulative distribution
*
> * @Deprecated 1.18.0
* @param float $probability
> *
* @param float $mean
> * @see Statistical\Distributions\LogNormal::inverse()
* @param float $stdDev
> * Use the inverse() method in the Statistical\Distributions\LogNormal class instead
*
> *
< * @return float|string The result, or a string containing an error
> * @return array|float|string The result, or a string containing an error
*
* @TODO Try implementing P J Acklam's refinement algorithm for greater
* accuracy if I can get my head round the mathematics
* (as described at) http://home.online.no/~pjacklam/notes/invnorm/
*/
public static function LOGINV($probability, $mean, $stdDev)
{
< $probability = Functions::flattenSingleValue($probability);
< $mean = Functions::flattenSingleValue($mean);
< $stdDev = Functions::flattenSingleValue($stdDev);
<
< if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
< if (($probability < 0) || ($probability > 1) || ($stdDev <= 0)) {
< return Functions::NAN();
< }
<
< return exp($mean + $stdDev * self::NORMSINV($probability));
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\LogNormal::inverse($probability, $mean, $stdDev);
}
/**
* LOGNORMDIST.
*
* Returns the cumulative lognormal distribution of x, where ln(x) is normally distributed
* with parameters mean and standard_dev.
*
> * @Deprecated 1.18.0
* @param float $value
> *
* @param float $mean
> * @see Statistical\Distributions\LogNormal::cumulative()
* @param float $stdDev
> * Use the cumulative() method in the Statistical\Distributions\LogNormal class instead
*
> *
< * @return float|string The result, or a string containing an error
> * @return array|float|string The result, or a string containing an error
*/
public static function LOGNORMDIST($value, $mean, $stdDev)
{
< $value = Functions::flattenSingleValue($value);
< $mean = Functions::flattenSingleValue($mean);
< $stdDev = Functions::flattenSingleValue($stdDev);
<
< if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
< if (($value <= 0) || ($stdDev <= 0)) {
< return Functions::NAN();
< }
<
< return self::NORMSDIST((log($value) - $mean) / $stdDev);
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\LogNormal::cumulative($value, $mean, $stdDev);
}
/**
* LOGNORM.DIST.
*
* Returns the lognormal distribution of x, where ln(x) is normally distributed
* with parameters mean and standard_dev.
*
> * @Deprecated 1.18.0
* @param float $value
> *
* @param float $mean
> * @see Statistical\Distributions\LogNormal::distribution()
* @param float $stdDev
> * Use the distribution() method in the Statistical\Distributions\LogNormal class instead
* @param bool $cumulative
> *
*
< * @return float|string The result, or a string containing an error
> * @return array|float|string The result, or a string containing an error
*/
public static function LOGNORMDIST2($value, $mean, $stdDev, $cumulative = false)
{
< $value = Functions::flattenSingleValue($value);
< $mean = Functions::flattenSingleValue($mean);
< $stdDev = Functions::flattenSingleValue($stdDev);
< $cumulative = (bool) Functions::flattenSingleValue($cumulative);
<
< if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
< if (($value <= 0) || ($stdDev <= 0)) {
< return Functions::NAN();
< }
<
< if ($cumulative === true) {
< return self::NORMSDIST2((log($value) - $mean) / $stdDev, true);
< }
<
< return (1 / (sqrt(2 * M_PI) * $stdDev * $value)) *
< exp(0 - ((log($value) - $mean) ** 2 / (2 * $stdDev ** 2)));
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\LogNormal::distribution($value, $mean, $stdDev, $cumulative);
}
/**
* MAX.
*
* MAX returns the value of the element of the values passed that has the highest value,
* with negative numbers considered smaller than positive numbers.
*
* Excel Function:
< * MAX(value1[,value2[, ...]])
> * max(value1[,value2[, ...]])
> *
> * @Deprecated 1.17.0
*
* @param mixed ...$args Data values
*
* @return float
> *
*/
> *@see Statistical\Maximum::max()
public static function MAX(...$args)
> * Use the MAX() method in the Statistical\Maximum class instead
{
< $returnValue = null;
<
< // Loop through arguments
< $aArgs = Functions::flattenArray($args);
< foreach ($aArgs as $arg) {
< // Is it a numeric value?
< if ((is_numeric($arg)) && (!is_string($arg))) {
< if (($returnValue === null) || ($arg > $returnValue)) {
< $returnValue = $arg;
< }
< }
< }
<
< if ($returnValue === null) {
< return 0;
< }
<
< return $returnValue;
> return Maximum::max(...$args);
}
/**
* MAXA.
*
* Returns the greatest value in a list of arguments, including numbers, text, and logical values
*
* Excel Function:
< * MAXA(value1[,value2[, ...]])
> * maxA(value1[,value2[, ...]])
> *
> * @Deprecated 1.17.0
*
* @param mixed ...$args Data values
*
* @return float
> *
*/
> *@see Statistical\Maximum::maxA()
public static function MAXA(...$args)
> * Use the MAXA() method in the Statistical\Maximum class instead
{
< $returnValue = null;
<
< // Loop through arguments
< $aArgs = Functions::flattenArray($args);
< foreach ($aArgs as $arg) {
< // Is it a numeric value?
< if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
< if (is_bool($arg)) {
< $arg = (int) $arg;
< } elseif (is_string($arg)) {
< $arg = 0;
< }
< if (($returnValue === null) || ($arg > $returnValue)) {
< $returnValue = $arg;
< }
< }
< }
<
< if ($returnValue === null) {
< return 0;
< }
<
< return $returnValue;
> return Maximum::maxA(...$args);
}
/**
* MAXIFS.
*
* Counts the maximum value within a range of cells that contain numbers within the list of arguments
*
* Excel Function:
* MAXIFS(max_range, criteria_range1, criteria1, [criteria_range2, criteria2], ...)
*
> * @Deprecated 1.17.0
* @param mixed $args Data range and criterias
> *
*
> * @see Statistical\Conditional::MAXIFS()
* @return float
> * Use the MAXIFS() method in the Statistical\Conditional class instead
*/
> *
public static function MAXIFS(...$args)
{
< $arrayList = $args;
<
< // Return value
< $returnValue = null;
<
< $maxArgs = Functions::flattenArray(array_shift($arrayList));
< $aArgsArray = [];
< $conditions = [];
<
< while (count($arrayList) > 0) {
< $aArgsArray[] = Functions::flattenArray(array_shift($arrayList));
< $conditions[] = Functions::ifCondition(array_shift($arrayList));
< }
<
< // Loop through each arg and see if arguments and conditions are true
< foreach ($maxArgs as $index => $value) {
< $valid = true;
<
< foreach ($conditions as $cidx => $condition) {
< $arg = $aArgsArray[$cidx][$index];
<
< // Loop through arguments
< if (!is_numeric($arg)) {
< $arg = Calculation::wrapResult(strtoupper($arg));
< }
< $testCondition = '=' . $arg . $condition;
< if (!Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
< // Is not a value within our criteria
< $valid = false;
<
< break; // if false found, don't need to check other conditions
< }
< }
<
< if ($valid) {
< $returnValue = $returnValue === null ? $value : max($value, $returnValue);
< }
< }
<
< // Return
< return $returnValue;
> return Conditional::MAXIFS(...$args);
}
/**
* MEDIAN.
*
* Returns the median of the given numbers. The median is the number in the middle of a set of numbers.
*
* Excel Function:
* MEDIAN(value1[,value2[, ...]])
*
> * @Deprecated 1.18.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\Averages::median()
* @return float|string The result, or a string containing an error
> * Use the median() method in the Statistical\Averages class instead
*/
> *
public static function MEDIAN(...$args)
{
< $returnValue = Functions::NAN();
<
< $mArgs = [];
< // Loop through arguments
< $aArgs = Functions::flattenArray($args);
< foreach ($aArgs as $arg) {
< // Is it a numeric value?
< if ((is_numeric($arg)) && (!is_string($arg))) {
< $mArgs[] = $arg;
< }
< }
<
< $mValueCount = count($mArgs);
< if ($mValueCount > 0) {
< sort($mArgs, SORT_NUMERIC);
< $mValueCount = $mValueCount / 2;
< if ($mValueCount == floor($mValueCount)) {
< $returnValue = ($mArgs[$mValueCount--] + $mArgs[$mValueCount]) / 2;
< } else {
< $mValueCount = floor($mValueCount);
< $returnValue = $mArgs[$mValueCount];
< }
< }
<
< return $returnValue;
> return Statistical\Averages::median(...$args);
}
/**
* MIN.
*
* MIN returns the value of the element of the values passed that has the smallest value,
* with negative numbers considered smaller than positive numbers.
*
* Excel Function:
* MIN(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
* @return float
> *
*/
> *@see Statistical\Minimum::min()
public static function MIN(...$args)
> * Use the min() method in the Statistical\Minimum class instead
{
< $returnValue = null;
<
< // Loop through arguments
< $aArgs = Functions::flattenArray($args);
< foreach ($aArgs as $arg) {
< // Is it a numeric value?
< if ((is_numeric($arg)) && (!is_string($arg))) {
< if (($returnValue === null) || ($arg < $returnValue)) {
< $returnValue = $arg;
< }
< }
< }
<
< if ($returnValue === null) {
< return 0;
< }
<
< return $returnValue;
> return Minimum::min(...$args);
}
/**
* MINA.
*
* Returns the smallest value in a list of arguments, including numbers, text, and logical values
*
* Excel Function:
* MINA(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
* @return float
> *
*/
> *@see Statistical\Minimum::minA()
public static function MINA(...$args)
> * Use the minA() method in the Statistical\Minimum class instead
{
< $returnValue = null;
<
< // Loop through arguments
< $aArgs = Functions::flattenArray($args);
< foreach ($aArgs as $arg) {
< // Is it a numeric value?
< if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
< if (is_bool($arg)) {
< $arg = (int) $arg;
< } elseif (is_string($arg)) {
< $arg = 0;
< }
< if (($returnValue === null) || ($arg < $returnValue)) {
< $returnValue = $arg;
< }
< }
< }
<
< if ($returnValue === null) {
< return 0;
< }
<
< return $returnValue;
> return Minimum::minA(...$args);
}
/**
* MINIFS.
*
* Returns the minimum value within a range of cells that contain numbers within the list of arguments
*
* Excel Function:
* MINIFS(min_range, criteria_range1, criteria1, [criteria_range2, criteria2], ...)
*
> * @Deprecated 1.17.0
* @param mixed $args Data range and criterias
> *
*
> * @see Statistical\Conditional::MINIFS()
* @return float
> * Use the MINIFS() method in the Statistical\Conditional class instead
*/
> *
public static function MINIFS(...$args)
{
< $arrayList = $args;
<
< // Return value
< $returnValue = null;
<
< $minArgs = Functions::flattenArray(array_shift($arrayList));
< $aArgsArray = [];
< $conditions = [];
<
< while (count($arrayList) > 0) {
< $aArgsArray[] = Functions::flattenArray(array_shift($arrayList));
< $conditions[] = Functions::ifCondition(array_shift($arrayList));
< }
<
< // Loop through each arg and see if arguments and conditions are true
< foreach ($minArgs as $index => $value) {
< $valid = true;
<
< foreach ($conditions as $cidx => $condition) {
< $arg = $aArgsArray[$cidx][$index];
<
< // Loop through arguments
< if (!is_numeric($arg)) {
< $arg = Calculation::wrapResult(strtoupper($arg));
< }
< $testCondition = '=' . $arg . $condition;
< if (!Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
< // Is not a value within our criteria
< $valid = false;
<
< break; // if false found, don't need to check other conditions
< }
< }
<
< if ($valid) {
< $returnValue = $returnValue === null ? $value : min($value, $returnValue);
< }
< }
<
< // Return
< return $returnValue;
< }
<
< //
< // Special variant of array_count_values that isn't limited to strings and integers,
< // but can work with floating point numbers as values
< //
< private static function modeCalc($data)
< {
< $frequencyArray = [];
< $index = 0;
< $maxfreq = 0;
< $maxfreqkey = '';
< $maxfreqdatum = '';
< foreach ($data as $datum) {
< $found = false;
< ++$index;
< foreach ($frequencyArray as $key => $value) {
< if ((string) $value['value'] == (string) $datum) {
< ++$frequencyArray[$key]['frequency'];
< $freq = $frequencyArray[$key]['frequency'];
< if ($freq > $maxfreq) {
< $maxfreq = $freq;
< $maxfreqkey = $key;
< $maxfreqdatum = $datum;
< } elseif ($freq == $maxfreq) {
< if ($frequencyArray[$key]['index'] < $frequencyArray[$maxfreqkey]['index']) {
< $maxfreqkey = $key;
< $maxfreqdatum = $datum;
< }
< }
< $found = true;
<
< break;
< }
< }
< if (!$found) {
< $frequencyArray[] = [
< 'value' => $datum,
< 'frequency' => 1,
< 'index' => $index,
< ];
< }
< }
<
< if ($maxfreq <= 1) {
< return Functions::NA();
< }
<
< return $maxfreqdatum;
> return Conditional::MINIFS(...$args);
}
/**
* MODE.
*
* Returns the most frequently occurring, or repetitive, value in an array or range of data
*
* Excel Function:
* MODE(value1[,value2[, ...]])
*
> * @Deprecated 1.18.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\Averages::mode()
* @return float|string The result, or a string containing an error
> * Use the mode() method in the Statistical\Averages class instead
*/
> *
public static function MODE(...$args)
{
< $returnValue = Functions::NA();
<
< // Loop through arguments
< $aArgs = Functions::flattenArray($args);
<
< $mArgs = [];
< foreach ($aArgs as $arg) {
< // Is it a numeric value?
< if ((is_numeric($arg)) && (!is_string($arg))) {
< $mArgs[] = $arg;
< }
< }
<
< if (!empty($mArgs)) {
< return self::modeCalc($mArgs);
< }
<
< return $returnValue;
> return Statistical\Averages::mode(...$args);
}
/**
* NEGBINOMDIST.
*
* Returns the negative binomial distribution. NEGBINOMDIST returns the probability that
* there will be number_f failures before the number_s-th success, when the constant
* probability of a success is probability_s. This function is similar to the binomial
* distribution, except that the number of successes is fixed, and the number of trials is
* variable. Like the binomial, trials are assumed to be independent.
*
< * @param float $failures Number of Failures
< * @param float $successes Threshold number of Successes
< * @param float $probability Probability of success on each trial
> * @Deprecated 1.18.0
*
< * @return float|string The result, or a string containing an error
> * @see Statistical\Distributions\Binomial::negative()
> * Use the negative() method in the Statistical\Distributions\Binomial class instead
> *
> * @param mixed $failures Number of Failures
> * @param mixed $successes Threshold number of Successes
> * @param mixed $probability Probability of success on each trial
> *
> * @return array|float|string The result, or a string containing an error
*/
public static function NEGBINOMDIST($failures, $successes, $probability)
{
< $failures = floor(Functions::flattenSingleValue($failures));
< $successes = floor(Functions::flattenSingleValue($successes));
< $probability = Functions::flattenSingleValue($probability);
<
< if ((is_numeric($failures)) && (is_numeric($successes)) && (is_numeric($probability))) {
< if (($failures < 0) || ($successes < 1)) {
< return Functions::NAN();
< } elseif (($probability < 0) || ($probability > 1)) {
< return Functions::NAN();
< }
< if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
< if (($failures + $successes - 1) <= 0) {
< return Functions::NAN();
< }
< }
<
< return (MathTrig::COMBIN($failures + $successes - 1, $successes - 1)) * ($probability ** $successes) * ((1 - $probability) ** $failures);
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\Binomial::negative($failures, $successes, $probability);
}
/**
* NORMDIST.
*
* Returns the normal distribution for the specified mean and standard deviation. This
* function has a very wide range of applications in statistics, including hypothesis
* testing.
*
< * @param float $value
< * @param float $mean Mean Value
< * @param float $stdDev Standard Deviation
< * @param bool $cumulative
> * @Deprecated 1.18.0
*
< * @return float|string The result, or a string containing an error
> * @see Statistical\Distributions\Normal::distribution()
> * Use the distribution() method in the Statistical\Distributions\Normal class instead
> *
> * @param mixed $value
> * @param mixed $mean Mean Value
> * @param mixed $stdDev Standard Deviation
> * @param mixed $cumulative
> *
> * @return array|float|string The result, or a string containing an error
*/
public static function NORMDIST($value, $mean, $stdDev, $cumulative)
{
< $value = Functions::flattenSingleValue($value);
< $mean = Functions::flattenSingleValue($mean);
< $stdDev = Functions::flattenSingleValue($stdDev);
<
< if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
< if ($stdDev < 0) {
< return Functions::NAN();
< }
< if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
< if ($cumulative) {
< return 0.5 * (1 + Engineering::erfVal(($value - $mean) / ($stdDev * sqrt(2))));
< }
<
< return (1 / (self::SQRT2PI * $stdDev)) * exp(0 - (($value - $mean) ** 2 / (2 * ($stdDev * $stdDev))));
< }
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\Normal::distribution($value, $mean, $stdDev, $cumulative);
}
/**
* NORMINV.
*
* Returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.
*
< * @param float $probability
< * @param float $mean Mean Value
< * @param float $stdDev Standard Deviation
> * @Deprecated 1.18.0
*
< * @return float|string The result, or a string containing an error
> * @see Statistical\Distributions\Normal::inverse()
> * Use the inverse() method in the Statistical\Distributions\Normal class instead
> *
> * @param mixed $probability
> * @param mixed $mean Mean Value
> * @param mixed $stdDev Standard Deviation
> *
> * @return array|float|string The result, or a string containing an error
*/
public static function NORMINV($probability, $mean, $stdDev)
{
< $probability = Functions::flattenSingleValue($probability);
< $mean = Functions::flattenSingleValue($mean);
< $stdDev = Functions::flattenSingleValue($stdDev);
<
< if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
< if (($probability < 0) || ($probability > 1)) {
< return Functions::NAN();
< }
< if ($stdDev < 0) {
< return Functions::NAN();
< }
<
< return (self::inverseNcdf($probability) * $stdDev) + $mean;
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\Normal::inverse($probability, $mean, $stdDev);
}
/**
* NORMSDIST.
*
* Returns the standard normal cumulative distribution function. The distribution has
* a mean of 0 (zero) and a standard deviation of one. Use this function in place of a
* table of standard normal curve areas.
*
< * @param float $value
> * @Deprecated 1.18.0
*
< * @return float|string The result, or a string containing an error
> * @see Statistical\Distributions\StandardNormal::cumulative()
> * Use the cumulative() method in the Statistical\Distributions\StandardNormal class instead
> *
> * @param mixed $value
> *
> * @return array|float|string The result, or a string containing an error
*/
public static function NORMSDIST($value)
{
< $value = Functions::flattenSingleValue($value);
< if (!is_numeric($value)) {
< return Functions::VALUE();
< }
<
< return self::NORMDIST($value, 0, 1, true);
> return Statistical\Distributions\StandardNormal::cumulative($value);
}
/**
* NORM.S.DIST.
*
* Returns the standard normal cumulative distribution function. The distribution has
* a mean of 0 (zero) and a standard deviation of one. Use this function in place of a
* table of standard normal curve areas.
*
< * @param float $value
< * @param bool $cumulative
> * @Deprecated 1.18.0
*
< * @return float|string The result, or a string containing an error
> * @see Statistical\Distributions\StandardNormal::distribution()
> * Use the distribution() method in the Statistical\Distributions\StandardNormal class instead
> *
> * @param mixed $value
> * @param mixed $cumulative
> *
> * @return array|float|string The result, or a string containing an error
*/
public static function NORMSDIST2($value, $cumulative)
{
< $value = Functions::flattenSingleValue($value);
< if (!is_numeric($value)) {
< return Functions::VALUE();
< }
< $cumulative = (bool) Functions::flattenSingleValue($cumulative);
<
< return self::NORMDIST($value, 0, 1, $cumulative);
> return Statistical\Distributions\StandardNormal::distribution($value, $cumulative);
}
/**
* NORMSINV.
*
* Returns the inverse of the standard normal cumulative distribution
*
< * @param float $value
> * @Deprecated 1.18.0
*
< * @return float|string The result, or a string containing an error
> * @see Statistical\Distributions\StandardNormal::inverse()
> * Use the inverse() method in the Statistical\Distributions\StandardNormal class instead
> *
> * @param mixed $value
> *
> * @return array|float|string The result, or a string containing an error
*/
public static function NORMSINV($value)
{
< return self::NORMINV($value, 0, 1);
> return Statistical\Distributions\StandardNormal::inverse($value);
}
/**
* PERCENTILE.
*
* Returns the nth percentile of values in a range..
*
* Excel Function:
* PERCENTILE(value1[,value2[, ...]],entry)
*
> * @Deprecated 1.18.0
* @param mixed $args Data values
> *
*
> * @see Statistical\Percentiles::PERCENTILE()
* @return float|string The result, or a string containing an error
> * Use the PERCENTILE() method in the Statistical\Percentiles class instead
*/
> *
public static function PERCENTILE(...$args)
{
< $aArgs = Functions::flattenArray($args);
<
< // Calculate
< $entry = array_pop($aArgs);
<
< if ((is_numeric($entry)) && (!is_string($entry))) {
< if (($entry < 0) || ($entry > 1)) {
< return Functions::NAN();
< }
< $mArgs = [];
< foreach ($aArgs as $arg) {
< // Is it a numeric value?
< if ((is_numeric($arg)) && (!is_string($arg))) {
< $mArgs[] = $arg;
< }
< }
< $mValueCount = count($mArgs);
< if ($mValueCount > 0) {
< sort($mArgs);
< $count = self::COUNT($mArgs);
< $index = $entry * ($count - 1);
< $iBase = floor($index);
< if ($index == $iBase) {
< return $mArgs[$index];
< }
< $iNext = $iBase + 1;
< $iProportion = $index - $iBase;
<
< return $mArgs[$iBase] + (($mArgs[$iNext] - $mArgs[$iBase]) * $iProportion);
< }
< }
<
< return Functions::VALUE();
> return Statistical\Percentiles::PERCENTILE(...$args);
}
/**
* PERCENTRANK.
*
* Returns the rank of a value in a data set as a percentage of the data set.
< *
< * @param float[] $valueSet An array of, or a reference to, a list of numbers
< * @param int $value the number whose rank you want to find
< * @param int $significance the number of significant digits for the returned percentage value
> * Note that the returned rank is simply rounded to the appropriate significant digits,
> * rather than floored (as MS Excel), so value 3 for a value set of 1, 2, 3, 4 will return
> * 0.667 rather than 0.666
> *
> * @Deprecated 1.18.0
> *
> * @see Statistical\Percentiles::PERCENTRANK()
> * Use the PERCENTRANK() method in the Statistical\Percentiles class instead
> *
> * @param mixed $valueSet An array of, or a reference to, a list of numbers
> * @param mixed $value the number whose rank you want to find
> * @param mixed $significance the number of significant digits for the returned percentage value
*
* @return float|string (string if result is an error)
*/
public static function PERCENTRANK($valueSet, $value, $significance = 3)
{
< $valueSet = Functions::flattenArray($valueSet);
< $value = Functions::flattenSingleValue($value);
< $significance = ($significance === null) ? 3 : (int) Functions::flattenSingleValue($significance);
<
< foreach ($valueSet as $key => $valueEntry) {
< if (!is_numeric($valueEntry)) {
< unset($valueSet[$key]);
< }
< }
< sort($valueSet, SORT_NUMERIC);
< $valueCount = count($valueSet);
< if ($valueCount == 0) {
< return Functions::NAN();
< }
<
< $valueAdjustor = $valueCount - 1;
< if (($value < $valueSet[0]) || ($value > $valueSet[$valueAdjustor])) {
< return Functions::NA();
< }
<
< $pos = array_search($value, $valueSet);
< if ($pos === false) {
< $pos = 0;
< $testValue = $valueSet[0];
< while ($testValue < $value) {
< $testValue = $valueSet[++$pos];
< }
< --$pos;
< $pos += (($value - $valueSet[$pos]) / ($testValue - $valueSet[$pos]));
< }
<
< return round($pos / $valueAdjustor, $significance);
> return Statistical\Percentiles::PERCENTRANK($valueSet, $value, $significance);
}
/**
* PERMUT.
*
* Returns the number of permutations for a given number of objects that can be
* selected from number objects. A permutation is any set or subset of objects or
* events where internal order is significant. Permutations are different from
* combinations, for which the internal order is not significant. Use this function
* for lottery-style probability calculations.
*
> * @Deprecated 1.17.0
* @param int $numObjs Number of different objects
> *
* @param int $numInSet Number of objects in each permutation
> * @see Statistical\Permutations::PERMUT()
*
> * Use the PERMUT() method in the Statistical\Permutations class instead
* @return int|string Number of permutations, or a string containing an error
> *
< * @return int|string Number of permutations, or a string containing an error
> * @return array|float|int|string Number of permutations, or a string containing an error
public static function PERMUT($numObjs, $numInSet)
{
< $numObjs = Functions::flattenSingleValue($numObjs);
< $numInSet = Functions::flattenSingleValue($numInSet);
<
< if ((is_numeric($numObjs)) && (is_numeric($numInSet))) {
< $numInSet = floor($numInSet);
< if ($numObjs < $numInSet) {
< return Functions::NAN();
< }
<
< return round(MathTrig::FACT($numObjs) / MathTrig::FACT($numObjs - $numInSet));
< }
<
< return Functions::VALUE();
> return Permutations::PERMUT($numObjs, $numInSet);
}
/**
* POISSON.
*
* Returns the Poisson distribution. A common application of the Poisson distribution
* is predicting the number of events over a specific time, such as the number of
* cars arriving at a toll plaza in 1 minute.
*
< * @param float $value
< * @param float $mean Mean Value
< * @param bool $cumulative
> * @Deprecated 1.18.0
*
< * @return float|string The result, or a string containing an error
> * @see Statistical\Distributions\Poisson::distribution()
> * Use the distribution() method in the Statistical\Distributions\Poisson class instead
> *
> * @param mixed $value
> * @param mixed $mean Mean Value
> * @param mixed $cumulative
> *
> * @return array|float|string The result, or a string containing an error
*/
public static function POISSON($value, $mean, $cumulative)
{
< $value = Functions::flattenSingleValue($value);
< $mean = Functions::flattenSingleValue($mean);
<
< if ((is_numeric($value)) && (is_numeric($mean))) {
< if (($value < 0) || ($mean <= 0)) {
< return Functions::NAN();
< }
< if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
< if ($cumulative) {
< $summer = 0;
< $floor = floor($value);
< for ($i = 0; $i <= $floor; ++$i) {
< $summer += $mean ** $i / MathTrig::FACT($i);
< }
<
< return exp(0 - $mean) * $summer;
< }
<
< return (exp(0 - $mean) * $mean ** $value) / MathTrig::FACT($value);
< }
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\Poisson::distribution($value, $mean, $cumulative);
}
/**
* QUARTILE.
*
* Returns the quartile of a data set.
*
* Excel Function:
* QUARTILE(value1[,value2[, ...]],entry)
*
> * @Deprecated 1.18.0
* @param mixed $args Data values
> *
*
> * @see Statistical\Percentiles::QUARTILE()
* @return float|string The result, or a string containing an error
> * Use the QUARTILE() method in the Statistical\Percentiles class instead
*/
> *
public static function QUARTILE(...$args)
{
< $aArgs = Functions::flattenArray($args);
<
< // Calculate
< $entry = floor(array_pop($aArgs));
<
< if ((is_numeric($entry)) && (!is_string($entry))) {
< $entry /= 4;
< if (($entry < 0) || ($entry > 1)) {
< return Functions::NAN();
< }
<
< return self::PERCENTILE($aArgs, $entry);
< }
<
< return Functions::VALUE();
> return Statistical\Percentiles::QUARTILE(...$args);
}
/**
* RANK.
*
* Returns the rank of a number in a list of numbers.
*
< * @param int $value the number whose rank you want to find
< * @param float[] $valueSet An array of, or a reference to, a list of numbers
< * @param int $order Order to sort the values in the value set
> * @Deprecated 1.18.0
> *
> * @see Statistical\Percentiles::RANK()
> * Use the RANK() method in the Statistical\Percentiles class instead
> *
> * @param mixed $value the number whose rank you want to find
> * @param mixed $valueSet An array of, or a reference to, a list of numbers
> * @param mixed $order Order to sort the values in the value set
*
* @return float|string The result, or a string containing an error
*/
public static function RANK($value, $valueSet, $order = 0)
{
< $value = Functions::flattenSingleValue($value);
< $valueSet = Functions::flattenArray($valueSet);
< $order = ($order === null) ? 0 : (int) Functions::flattenSingleValue($order);
<
< foreach ($valueSet as $key => $valueEntry) {
< if (!is_numeric($valueEntry)) {
< unset($valueSet[$key]);
< }
< }
<
< if ($order == 0) {
< rsort($valueSet, SORT_NUMERIC);
< } else {
< sort($valueSet, SORT_NUMERIC);
< }
< $pos = array_search($value, $valueSet);
< if ($pos === false) {
< return Functions::NA();
< }
<
< return ++$pos;
> return Statistical\Percentiles::RANK($value, $valueSet, $order);
}
/**
* RSQ.
*
* Returns the square of the Pearson product moment correlation coefficient through data points in known_y's and known_x's.
*
> * @Deprecated 1.18.0
* @param mixed[] $yValues Data Series Y
> *
* @param mixed[] $xValues Data Series X
> * @see Statistical\Trends::RSQ()
*
> * Use the RSQ() method in the Statistical\Trends class instead
* @return float|string The result, or a string containing an error
> *
*/
public static function RSQ($yValues, $xValues)
{
< if (!self::checkTrendArrays($yValues, $xValues)) {
< return Functions::VALUE();
< }
< $yValueCount = count($yValues);
< $xValueCount = count($xValues);
<
< if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
< return Functions::NA();
< } elseif ($yValueCount == 1) {
< return Functions::DIV0();
< }
<
< $bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
<
< return $bestFitLinear->getGoodnessOfFit();
> return Trends::RSQ($yValues, $xValues);
}
/**
* SKEW.
*
* Returns the skewness of a distribution. Skewness characterizes the degree of asymmetry
* of a distribution around its mean. Positive skewness indicates a distribution with an
* asymmetric tail extending toward more positive values. Negative skewness indicates a
* distribution with an asymmetric tail extending toward more negative values.
*
> * @Deprecated 1.18.0
* @param array ...$args Data Series
> *
*
> * @see Statistical\Deviations::skew()
* @return float|string The result, or a string containing an error
> * Use the skew() method in the Statistical\Deviations class instead
*/
> *
public static function SKEW(...$args)
{
< $aArgs = Functions::flattenArrayIndexed($args);
< $mean = self::AVERAGE($aArgs);
< $stdDev = self::STDEV($aArgs);
<
< $count = $summer = 0;
< // Loop through arguments
< foreach ($aArgs as $k => $arg) {
< if (
< (is_bool($arg)) &&
< (!Functions::isMatrixValue($k))
< ) {
< } else {
< // Is it a numeric value?
< if ((is_numeric($arg)) && (!is_string($arg))) {
< $summer += (($arg - $mean) / $stdDev) ** 3;
< ++$count;
< }
< }
< }
<
< if ($count > 2) {
< return $summer * ($count / (($count - 1) * ($count - 2)));
< }
<
< return Functions::DIV0();
> return Statistical\Deviations::skew(...$args);
}
/**
* SLOPE.
*
* Returns the slope of the linear regression line through data points in known_y's and known_x's.
*
> * @Deprecated 1.18.0
* @param mixed[] $yValues Data Series Y
> *
* @param mixed[] $xValues Data Series X
> * @see Statistical\Trends::SLOPE()
*
> * Use the SLOPE() method in the Statistical\Trends class instead
* @return float|string The result, or a string containing an error
> *
*/
public static function SLOPE($yValues, $xValues)
{
< if (!self::checkTrendArrays($yValues, $xValues)) {
< return Functions::VALUE();
< }
< $yValueCount = count($yValues);
< $xValueCount = count($xValues);
<
< if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
< return Functions::NA();
< } elseif ($yValueCount == 1) {
< return Functions::DIV0();
< }
<
< $bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
<
< return $bestFitLinear->getSlope();
> return Trends::SLOPE($yValues, $xValues);
}
/**
* SMALL.
*
* Returns the nth smallest value in a data set. You can use this function to
* select a value based on its relative standing.
*
* Excel Function:
* SMALL(value1[,value2[, ...]],entry)
*
> * @Deprecated 1.18.0
* @param mixed $args Data values
> *
*
> * @see Statistical\Size::small()
* @return float|string The result, or a string containing an error
> * Use the small() method in the Statistical\Size class instead
*/
> *
public static function SMALL(...$args)
{
< $aArgs = Functions::flattenArray($args);
<
< // Calculate
< $entry = array_pop($aArgs);
<
< if ((is_numeric($entry)) && (!is_string($entry))) {
< $entry = (int) floor($entry);
<
< $mArgs = [];
< foreach ($aArgs as $arg) {
< // Is it a numeric value?
< if ((is_numeric($arg)) && (!is_string($arg))) {
< $mArgs[] = $arg;
< }
< }
< $count = self::COUNT($mArgs);
< --$entry;
< if (($entry < 0) || ($entry >= $count) || ($count == 0)) {
< return Functions::NAN();
< }
< sort($mArgs);
<
< return $mArgs[$entry];
< }
<
< return Functions::VALUE();
> return Statistical\Size::small(...$args);
}
/**
* STANDARDIZE.
*
* Returns a normalized value from a distribution characterized by mean and standard_dev.
*
> * @Deprecated 1.18.0
* @param float $value Value to normalize
> *
* @param float $mean Mean Value
> * @see Statistical\Standardize::execute()
* @param float $stdDev Standard Deviation
> * Use the execute() method in the Statistical\Standardize class instead
*
> *
< * @return float|string Standardized value, or a string containing an error
> * @return array|float|string Standardized value, or a string containing an error
*/
public static function STANDARDIZE($value, $mean, $stdDev)
{
< $value = Functions::flattenSingleValue($value);
< $mean = Functions::flattenSingleValue($mean);
< $stdDev = Functions::flattenSingleValue($stdDev);
<
< if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
< if ($stdDev <= 0) {
< return Functions::NAN();
< }
<
< return ($value - $mean) / $stdDev;
< }
<
< return Functions::VALUE();
> return Statistical\Standardize::execute($value, $mean, $stdDev);
}
/**
* STDEV.
*
* Estimates standard deviation based on a sample. The standard deviation is a measure of how
* widely values are dispersed from the average value (the mean).
*
* Excel Function:
* STDEV(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\StandardDeviations::STDEV()
* @return float|string The result, or a string containing an error
> * Use the STDEV() method in the Statistical\StandardDeviations class instead
*/
> *
public static function STDEV(...$args)
{
< $aArgs = Functions::flattenArrayIndexed($args);
<
< // Return value
< $returnValue = null;
<
< $aMean = self::AVERAGE($aArgs);
< if ($aMean !== null) {
< $aCount = -1;
< foreach ($aArgs as $k => $arg) {
< if (
< (is_bool($arg)) &&
< ((!Functions::isCellValue($k)) || (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))
< ) {
< $arg = (int) $arg;
< }
< // Is it a numeric value?
< if ((is_numeric($arg)) && (!is_string($arg))) {
< if ($returnValue === null) {
< $returnValue = ($arg - $aMean) ** 2;
< } else {
< $returnValue += ($arg - $aMean) ** 2;
< }
< ++$aCount;
< }
< }
<
< // Return
< if (($aCount > 0) && ($returnValue >= 0)) {
< return sqrt($returnValue / $aCount);
< }
< }
<
< return Functions::DIV0();
> return StandardDeviations::STDEV(...$args);
}
/**
* STDEVA.
*
* Estimates standard deviation based on a sample, including numbers, text, and logical values
*
* Excel Function:
* STDEVA(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\StandardDeviations::STDEVA()
* @return float|string
> * Use the STDEVA() method in the Statistical\StandardDeviations class instead
*/
> *
public static function STDEVA(...$args)
{
< $aArgs = Functions::flattenArrayIndexed($args);
<
< $returnValue = null;
<
< $aMean = self::AVERAGEA($aArgs);
< if ($aMean !== null) {
< $aCount = -1;
< foreach ($aArgs as $k => $arg) {
< if (
< (is_bool($arg)) &&
< (!Functions::isMatrixValue($k))
< ) {
< } else {
< // Is it a numeric value?
< if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
< if (is_bool($arg)) {
< $arg = (int) $arg;
< } elseif (is_string($arg)) {
< $arg = 0;
< }
< if ($returnValue === null) {
< $returnValue = ($arg - $aMean) ** 2;
< } else {
< $returnValue += ($arg - $aMean) ** 2;
< }
< ++$aCount;
< }
< }
< }
<
< if (($aCount > 0) && ($returnValue >= 0)) {
< return sqrt($returnValue / $aCount);
< }
< }
<
< return Functions::DIV0();
> return StandardDeviations::STDEVA(...$args);
}
/**
* STDEVP.
*
* Calculates standard deviation based on the entire population
*
* Excel Function:
* STDEVP(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\StandardDeviations::STDEVP()
* @return float|string
> * Use the STDEVP() method in the Statistical\StandardDeviations class instead
*/
> *
public static function STDEVP(...$args)
{
< $aArgs = Functions::flattenArrayIndexed($args);
<
< $returnValue = null;
<
< $aMean = self::AVERAGE($aArgs);
< if ($aMean !== null) {
< $aCount = 0;
< foreach ($aArgs as $k => $arg) {
< if (
< (is_bool($arg)) &&
< ((!Functions::isCellValue($k)) || (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))
< ) {
< $arg = (int) $arg;
< }
< // Is it a numeric value?
< if ((is_numeric($arg)) && (!is_string($arg))) {
< if ($returnValue === null) {
< $returnValue = ($arg - $aMean) ** 2;
< } else {
< $returnValue += ($arg - $aMean) ** 2;
< }
< ++$aCount;
< }
< }
<
< if (($aCount > 0) && ($returnValue >= 0)) {
< return sqrt($returnValue / $aCount);
< }
< }
<
< return Functions::DIV0();
> return StandardDeviations::STDEVP(...$args);
}
/**
* STDEVPA.
*
* Calculates standard deviation based on the entire population, including numbers, text, and logical values
*
* Excel Function:
* STDEVPA(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\StandardDeviations::STDEVPA()
* @return float|string
> * Use the STDEVPA() method in the Statistical\StandardDeviations class instead
*/
> *
public static function STDEVPA(...$args)
{
< $aArgs = Functions::flattenArrayIndexed($args);
<
< $returnValue = null;
<
< $aMean = self::AVERAGEA($aArgs);
< if ($aMean !== null) {
< $aCount = 0;
< foreach ($aArgs as $k => $arg) {
< if (
< (is_bool($arg)) &&
< (!Functions::isMatrixValue($k))
< ) {
< } else {
< // Is it a numeric value?
< if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
< if (is_bool($arg)) {
< $arg = (int) $arg;
< } elseif (is_string($arg)) {
< $arg = 0;
< }
< if ($returnValue === null) {
< $returnValue = ($arg - $aMean) ** 2;
< } else {
< $returnValue += ($arg - $aMean) ** 2;
< }
< ++$aCount;
< }
< }
< }
<
< if (($aCount > 0) && ($returnValue >= 0)) {
< return sqrt($returnValue / $aCount);
< }
< }
<
< return Functions::DIV0();
> return StandardDeviations::STDEVPA(...$args);
}
/**
* STEYX.
*
> * @Deprecated 1.18.0
* Returns the standard error of the predicted y-value for each x in the regression.
> *
*
> * @see Statistical\Trends::STEYX()
* @param mixed[] $yValues Data Series Y
> * Use the STEYX() method in the Statistical\Trends class instead
* @param mixed[] $xValues Data Series X
> *
*
* @return float|string
*/
public static function STEYX($yValues, $xValues)
{
< if (!self::checkTrendArrays($yValues, $xValues)) {
< return Functions::VALUE();
< }
< $yValueCount = count($yValues);
< $xValueCount = count($xValues);
<
< if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
< return Functions::NA();
< } elseif ($yValueCount == 1) {
< return Functions::DIV0();
< }
<
< $bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
<
< return $bestFitLinear->getStdevOfResiduals();
> return Trends::STEYX($yValues, $xValues);
}
/**
* TDIST.
*
* Returns the probability of Student's T distribution.
*
> * @Deprecated 1.18.0
* @param float $value Value for the function
> *
* @param float $degrees degrees of freedom
> * @see Statistical\Distributions\StudentT::distribution()
* @param float $tails number of tails (1 or 2)
> * Use the distribution() method in the Statistical\Distributions\StudentT class instead
*
> *
< * @return float|string The result, or a string containing an error
> * @return array|float|string The result, or a string containing an error
*/
public static function TDIST($value, $degrees, $tails)
{
< $value = Functions::flattenSingleValue($value);
< $degrees = floor(Functions::flattenSingleValue($degrees));
< $tails = floor(Functions::flattenSingleValue($tails));
<
< if ((is_numeric($value)) && (is_numeric($degrees)) && (is_numeric($tails))) {
< if (($value < 0) || ($degrees < 1) || ($tails < 1) || ($tails > 2)) {
< return Functions::NAN();
< }
< // tdist, which finds the probability that corresponds to a given value
< // of t with k degrees of freedom. This algorithm is translated from a
< // pascal function on p81 of "Statistical Computing in Pascal" by D
< // Cooke, A H Craven & G M Clark (1985: Edward Arnold (Pubs.) Ltd:
< // London). The above Pascal algorithm is itself a translation of the
< // fortran algoritm "AS 3" by B E Cooper of the Atlas Computer
< // Laboratory as reported in (among other places) "Applied Statistics
< // Algorithms", editied by P Griffiths and I D Hill (1985; Ellis
< // Horwood Ltd.; W. Sussex, England).
< $tterm = $degrees;
< $ttheta = atan2($value, sqrt($tterm));
< $tc = cos($ttheta);
< $ts = sin($ttheta);
<
< if (($degrees % 2) == 1) {
< $ti = 3;
< $tterm = $tc;
< } else {
< $ti = 2;
< $tterm = 1;
< }
<
< $tsum = $tterm;
< while ($ti < $degrees) {
< $tterm *= $tc * $tc * ($ti - 1) / $ti;
< $tsum += $tterm;
< $ti += 2;
< }
< $tsum *= $ts;
< if (($degrees % 2) == 1) {
< $tsum = Functions::M_2DIVPI * ($tsum + $ttheta);
< }
< $tValue = 0.5 * (1 + $tsum);
< if ($tails == 1) {
< return 1 - abs($tValue);
< }
<
< return 1 - abs((1 - $tValue) - $tValue);
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\StudentT::distribution($value, $degrees, $tails);
}
/**
* TINV.
*
< * Returns the one-tailed probability of the chi-squared distribution.
> * Returns the one-tailed probability of the Student-T distribution.
> *
> * @Deprecated 1.18.0
> *
> * @see Statistical\Distributions\StudentT::inverse()
> * Use the inverse() method in the Statistical\Distributions\StudentT class instead
*
* @param float $probability Probability for the function
* @param float $degrees degrees of freedom
*
< * @return float|string The result, or a string containing an error
> * @return array|float|string The result, or a string containing an error
*/
public static function TINV($probability, $degrees)
{
< $probability = Functions::flattenSingleValue($probability);
< $degrees = floor(Functions::flattenSingleValue($degrees));
<
< if ((is_numeric($probability)) && (is_numeric($degrees))) {
< $xLo = 100;
< $xHi = 0;
<
< $x = $xNew = 1;
< $dx = 1;
< $i = 0;
<
< while ((abs($dx) > Functions::PRECISION) && ($i++ < self::MAX_ITERATIONS)) {
< // Apply Newton-Raphson step
< $result = self::TDIST($x, $degrees, 2);
< $error = $result - $probability;
< if ($error == 0.0) {
< $dx = 0;
< } elseif ($error < 0.0) {
< $xLo = $x;
< } else {
< $xHi = $x;
< }
< // Avoid division by zero
< if ($result != 0.0) {
< $dx = $error / $result;
< $xNew = $x - $dx;
< }
< // If the NR fails to converge (which for example may be the
< // case if the initial guess is too rough) we apply a bisection
< // step to determine a more narrow interval around the root.
< if (($xNew < $xLo) || ($xNew > $xHi) || ($result == 0.0)) {
< $xNew = ($xLo + $xHi) / 2;
< $dx = $xNew - $x;
< }
< $x = $xNew;
< }
< if ($i == self::MAX_ITERATIONS) {
< return Functions::NA();
< }
<
< return round($x, 12);
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\StudentT::inverse($probability, $degrees);
}
/**
* TREND.
*
* Returns values along a linear Trend
*
> * @Deprecated 1.18.0
* @param mixed[] $yValues Data Series Y
> *
* @param mixed[] $xValues Data Series X
> * @see Statistical\Trends::TREND()
* @param mixed[] $newValues Values of X for which we want to find Y
> * Use the TREND() method in the Statistical\Trends class instead
* @param bool $const a logical value specifying whether to force the intersect to equal 0
> *
*
< * @return array of float
> * @return float[]
*/
public static function TREND($yValues, $xValues = [], $newValues = [], $const = true)
{
< $yValues = Functions::flattenArray($yValues);
< $xValues = Functions::flattenArray($xValues);
< $newValues = Functions::flattenArray($newValues);
< $const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const);
<
< $bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues, $const);
< if (empty($newValues)) {
< $newValues = $bestFitLinear->getXValues();
< }
<
< $returnArray = [];
< foreach ($newValues as $xValue) {
< $returnArray[0][] = $bestFitLinear->getValueOfYForX($xValue);
< }
<
< return $returnArray;
> return Trends::TREND($yValues, $xValues, $newValues, $const);
}
/**
* TRIMMEAN.
*
* Returns the mean of the interior of a data set. TRIMMEAN calculates the mean
* taken by excluding a percentage of data points from the top and bottom tails
* of a data set.
*
* Excel Function:
* TRIMEAN(value1[,value2[, ...]], $discard)
*
> * @Deprecated 1.18.0
* @param mixed $args Data values
> *
*
> *@see Statistical\Averages\Mean::trim()
* @return float|string
> * Use the trim() method in the Statistical\Averages\Mean class instead
*/
> *
public static function TRIMMEAN(...$args)
{
< $aArgs = Functions::flattenArray($args);
<
< // Calculate
< $percent = array_pop($aArgs);
<
< if ((is_numeric($percent)) && (!is_string($percent))) {
< if (($percent < 0) || ($percent > 1)) {
< return Functions::NAN();
< }
< $mArgs = [];
< foreach ($aArgs as $arg) {
< // Is it a numeric value?
< if ((is_numeric($arg)) && (!is_string($arg))) {
< $mArgs[] = $arg;
< }
< }
< $discard = floor(self::COUNT($mArgs) * $percent / 2);
< sort($mArgs);
< for ($i = 0; $i < $discard; ++$i) {
< array_pop($mArgs);
< array_shift($mArgs);
< }
<
< return self::AVERAGE($mArgs);
< }
<
< return Functions::VALUE();
> return Statistical\Averages\Mean::trim(...$args);
}
/**
* VARFunc.
*
* Estimates variance based on a sample.
*
* Excel Function:
* VAR(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
> *@see Statistical\Variances::VAR()
* @return float|string (string if result is an error)
> * Use the VAR() method in the Statistical\Variances class instead
*/
> *
public static function VARFunc(...$args)
{
< $returnValue = Functions::DIV0();
<
< $summerA = $summerB = 0;
<
< // Loop through arguments
< $aArgs = Functions::flattenArray($args);
< $aCount = 0;
< foreach ($aArgs as $arg) {
< if (is_bool($arg)) {
< $arg = (int) $arg;
< }
< // Is it a numeric value?
< if ((is_numeric($arg)) && (!is_string($arg))) {
< $summerA += ($arg * $arg);
< $summerB += $arg;
< ++$aCount;
< }
< }
<
< if ($aCount > 1) {
< $summerA *= $aCount;
< $summerB *= $summerB;
< $returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1));
< }
<
< return $returnValue;
> return Variances::VAR(...$args);
}
/**
* VARA.
*
* Estimates variance based on a sample, including numbers, text, and logical values
*
* Excel Function:
* VARA(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\Variances::VARA()
* @return float|string (string if result is an error)
> * Use the VARA() method in the Statistical\Variances class instead
*/
> *
public static function VARA(...$args)
{
< $returnValue = Functions::DIV0();
<
< $summerA = $summerB = 0;
<
< // Loop through arguments
< $aArgs = Functions::flattenArrayIndexed($args);
< $aCount = 0;
< foreach ($aArgs as $k => $arg) {
< if (
< (is_string($arg)) &&
< (Functions::isValue($k))
< ) {
< return Functions::VALUE();
< } elseif (
< (is_string($arg)) &&
< (!Functions::isMatrixValue($k))
< ) {
< } else {
< // Is it a numeric value?
< if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
< if (is_bool($arg)) {
< $arg = (int) $arg;
< } elseif (is_string($arg)) {
< $arg = 0;
< }
< $summerA += ($arg * $arg);
< $summerB += $arg;
< ++$aCount;
< }
< }
< }
<
< if ($aCount > 1) {
< $summerA *= $aCount;
< $summerB *= $summerB;
< $returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1));
< }
<
< return $returnValue;
> return Variances::VARA(...$args);
}
/**
* VARP.
*
* Calculates variance based on the entire population
*
* Excel Function:
* VARP(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\Variances::VARP()
* @return float|string (string if result is an error)
> * Use the VARP() method in the Statistical\Variances class instead
*/
> *
public static function VARP(...$args)
{
< // Return value
< $returnValue = Functions::DIV0();
<
< $summerA = $summerB = 0;
<
< // Loop through arguments
< $aArgs = Functions::flattenArray($args);
< $aCount = 0;
< foreach ($aArgs as $arg) {
< if (is_bool($arg)) {
< $arg = (int) $arg;
< }
< // Is it a numeric value?
< if ((is_numeric($arg)) && (!is_string($arg))) {
< $summerA += ($arg * $arg);
< $summerB += $arg;
< ++$aCount;
< }
< }
<
< if ($aCount > 0) {
< $summerA *= $aCount;
< $summerB *= $summerB;
< $returnValue = ($summerA - $summerB) / ($aCount * $aCount);
< }
<
< return $returnValue;
> return Variances::VARP(...$args);
}
/**
* VARPA.
*
* Calculates variance based on the entire population, including numbers, text, and logical values
*
* Excel Function:
* VARPA(value1[,value2[, ...]])
*
> * @Deprecated 1.17.0
* @param mixed ...$args Data values
> *
*
> * @see Statistical\Variances::VARPA()
* @return float|string (string if result is an error)
> * Use the VARPA() method in the Statistical\Variances class instead
*/
> *
public static function VARPA(...$args)
{
< $returnValue = Functions::DIV0();
<
< $summerA = $summerB = 0;
<
< // Loop through arguments
< $aArgs = Functions::flattenArrayIndexed($args);
< $aCount = 0;
< foreach ($aArgs as $k => $arg) {
< if (
< (is_string($arg)) &&
< (Functions::isValue($k))
< ) {
< return Functions::VALUE();
< } elseif (
< (is_string($arg)) &&
< (!Functions::isMatrixValue($k))
< ) {
< } else {
< // Is it a numeric value?
< if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
< if (is_bool($arg)) {
< $arg = (int) $arg;
< } elseif (is_string($arg)) {
< $arg = 0;
< }
< $summerA += ($arg * $arg);
< $summerB += $arg;
< ++$aCount;
< }
< }
< }
<
< if ($aCount > 0) {
< $summerA *= $aCount;
< $summerB *= $summerB;
< $returnValue = ($summerA - $summerB) / ($aCount * $aCount);
< }
<
< return $returnValue;
> return Variances::VARPA(...$args);
}
/**
* WEIBULL.
*
* Returns the Weibull distribution. Use this distribution in reliability
* analysis, such as calculating a device's mean time to failure.
*
> * @Deprecated 1.18.0
* @param float $value
> *
* @param float $alpha Alpha Parameter
> * @see Statistical\Distributions\Weibull::distribution()
* @param float $beta Beta Parameter
> * Use the distribution() method in the Statistical\Distributions\Weibull class instead
* @param bool $cumulative
> *
*
< * @return float|string (string if result is an error)
> * @return array|float|string (string if result is an error)
*/
public static function WEIBULL($value, $alpha, $beta, $cumulative)
{
< $value = Functions::flattenSingleValue($value);
< $alpha = Functions::flattenSingleValue($alpha);
< $beta = Functions::flattenSingleValue($beta);
<
< if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta))) {
< if (($value < 0) || ($alpha <= 0) || ($beta <= 0)) {
< return Functions::NAN();
< }
< if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
< if ($cumulative) {
< return 1 - exp(0 - ($value / $beta) ** $alpha);
< }
<
< return ($alpha / $beta ** $alpha) * $value ** ($alpha - 1) * exp(0 - ($value / $beta) ** $alpha);
< }
< }
<
< return Functions::VALUE();
> return Statistical\Distributions\Weibull::distribution($value, $alpha, $beta, $cumulative);
}
/**
* ZTEST.
*
< * Returns the Weibull distribution. Use this distribution in reliability
< * analysis, such as calculating a device's mean time to failure.
> * Returns the one-tailed P-value of a z-test.
> *
> * For a given hypothesized population mean, x, Z.TEST returns the probability that the sample mean would be
> * greater than the average of observations in the data set (array) — that is, the observed sample mean.
> *
> * @Deprecated 1.18.0
> *
> * @see Statistical\Distributions\StandardNormal::zTest()
> * Use the zTest() method in the Statistical\Distributions\StandardNormal class instead
*
* @param float $dataSet
* @param float $m0 Alpha Parameter
* @param float $sigma Beta Parameter
*
< * @return float|string (string if result is an error)
> * @return array|float|string (string if result is an error)
*/
public static function ZTEST($dataSet, $m0, $sigma = null)
{
< $dataSet = Functions::flattenArrayIndexed($dataSet);
< $m0 = Functions::flattenSingleValue($m0);
< $sigma = Functions::flattenSingleValue($sigma);
<
< if ($sigma === null) {
< $sigma = self::STDEV($dataSet);
< }
< $n = count($dataSet);
<
< return 1 - self::NORMSDIST((self::AVERAGE($dataSet) - $m0) / ($sigma / sqrt($n)));
> return Statistical\Distributions\StandardNormal::zTest($dataSet, $m0, $sigma);
}
}