Search moodle.org's
Developer Documentation
Developer Documentation
See Release Notes
Long Term Support Release
- Bug fixes for general core bugs in 3.9.x will end* 10 May 2021 (12 months).
- Bug fixes for security issues in 3.9.x will end* 8 May 2023 (36 months).
- PHP version: minimum PHP 7.2.0 Note: minimum PHP version has increased since Moodle 3.8. PHP 7.3.x and 7.4.x are supported too.
Differences Between: [Versions 39 and 311] [Versions 39 and 400] [Versions 39 and 401] [Versions 39 and 402] [Versions 39 and 403]
(no description)
| File Size: | 3773 lines (121 kb) |
| Included or required: | 0 times |
| Referenced: | 0 times |
| Includes or requires: | 0 files |
Defines 1 class
Statistical:: (87 methods):
checkTrendArrays()
incompleteBeta()
logBeta()
betaFraction()
logGamma()
incompleteGamma()
gamma()
inverseNcdf()
testAcceptedBoolean()
isAcceptedCountable()
AVEDEV()
AVERAGE()
AVERAGEA()
AVERAGEIF()
BETADIST()
BETAINV()
BINOMDIST()
CHIDIST()
CHIINV()
CONFIDENCE()
CORREL()
COUNT()
COUNTA()
COUNTBLANK()
COUNTIF()
COUNTIFS()
COVAR()
CRITBINOM()
DEVSQ()
EXPONDIST()
FISHER()
FISHERINV()
FORECAST()
GAMMADIST()
GAMMAINV()
GAMMALN()
GEOMEAN()
GROWTH()
HARMEAN()
HYPGEOMDIST()
INTERCEPT()
KURT()
LARGE()
LINEST()
LOGEST()
LOGINV()
LOGNORMDIST()
MAX()
MAXA()
MAXIFS()
MEDIAN()
MIN()
MINA()
MINIFS()
modeCalc()
MODE()
NEGBINOMDIST()
NORMDIST()
NORMINV()
NORMSDIST()
NORMSINV()
PERCENTILE()
PERCENTRANK()
PERMUT()
POISSON()
QUARTILE()
RANK()
RSQ()
SKEW()
SLOPE()
SMALL()
STANDARDIZE()
STDEV()
STDEVA()
STDEVP()
STDEVPA()
STEYX()
TDIST()
TINV()
TREND()
TRIMMEAN()
VARFunc()
VARA()
VARP()
VARPA()
WEIBULL()
ZTEST()
Class: Statistical - X-Ref
| checkTrendArrays(&$array1, &$array2) X-Ref |
| No description |
| incompleteBeta($x, $p, $q) X-Ref |
| Incomplete beta function. param: mixed $x require 0<=x<=1 param: mixed $p require p>0 param: mixed $q require q>0 author: Jaco van Kooten author: Paul Meagher return: float 0 if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow |
| logBeta($p, $q) X-Ref |
| The natural logarithm of the beta function. param: mixed $p require p>0 param: mixed $q require q>0 author: Jaco van Kooten return: float 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow |
| betaFraction($x, $p, $q) X-Ref |
| Evaluates of continued fraction part of incomplete beta function. Based on an idea from Numerical Recipes (W.H. Press et al, 1992). param: mixed $x param: mixed $p param: mixed $q author: Jaco van Kooten return: float |
| logGamma($x) X-Ref |
| No description |
| incompleteGamma($a, $x) X-Ref |
| No description |
| gamma($data) X-Ref |
| No description |
| inverseNcdf($p) X-Ref |
| No description |
| testAcceptedBoolean($arg, $k) X-Ref |
| 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 $k return: int|mixed |
| isAcceptedCountable($arg, $k) X-Ref |
param: mixed $arg param: mixed $k return: bool |
| AVEDEV(...$args) X-Ref |
| 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[, ...]]) param: mixed ...$args Data values return: float|string |
| AVERAGE(...$args) X-Ref |
| AVERAGE. Returns the average (arithmetic mean) of the arguments Excel Function: AVERAGE(value1[,value2[, ...]]) param: mixed ...$args Data values return: float|string |
| AVERAGEA(...$args) X-Ref |
| AVERAGEA. Returns the average of its arguments, including numbers, text, and logical values Excel Function: AVERAGEA(value1[,value2[, ...]]) param: mixed ...$args Data values return: float|string |
| AVERAGEIF($aArgs, $condition, $averageArgs = []) X-Ref |
| 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 param: string $condition the criteria that defines which cells will be checked param: mixed[] $averageArgs Data values return: float|string |
| BETADIST($value, $alpha, $beta, $rMin = 0, $rMax = 1) X-Ref |
| BETADIST. Returns the beta distribution. param: float $value Value at which you want to evaluate the distribution param: float $alpha Parameter to the distribution param: float $beta Parameter to the distribution param: mixed $rMin param: mixed $rMax return: float|string |
| BETAINV($probability, $alpha, $beta, $rMin = 0, $rMax = 1) X-Ref |
| BETAINV. Returns the inverse of the beta distribution. param: float $probability Probability at which you want to evaluate the distribution param: float $alpha Parameter to the distribution param: float $beta Parameter to the distribution param: float $rMin Minimum value param: float $rMax Maximum value return: float|string |
| BINOMDIST($value, $trials, $probability, $cumulative) X-Ref |
| 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 $cumulative return: float|string |
| CHIDIST($value, $degrees) X-Ref |
| CHIDIST. Returns the one-tailed probability of the chi-squared distribution. param: float $value Value for the function param: float $degrees degrees of freedom return: float|string |
| CHIINV($probability, $degrees) X-Ref |
| CHIINV. Returns the one-tailed probability of the chi-squared distribution. param: float $probability Probability for the function param: float $degrees degrees of freedom return: float|string |
| CONFIDENCE($alpha, $stdDev, $size) X-Ref |
| CONFIDENCE. Returns the confidence interval for a population mean param: float $alpha param: float $stdDev Standard Deviation param: float $size return: float|string |
| CORREL($yValues, $xValues = null) X-Ref |
| CORREL. Returns covariance, the average of the products of deviations for each data point pair. param: mixed $yValues array of mixed Data Series Y param: null|mixed $xValues array of mixed Data Series X return: float|string |
| COUNT(...$args) X-Ref |
| COUNT. Counts the number of cells that contain numbers within the list of arguments Excel Function: COUNT(value1[,value2[, ...]]) param: mixed ...$args Data values return: int |
| COUNTA(...$args) X-Ref |
| COUNTA. Counts the number of cells that are not empty within the list of arguments Excel Function: COUNTA(value1[,value2[, ...]]) param: mixed ...$args Data values return: int |
| COUNTBLANK(...$args) X-Ref |
| COUNTBLANK. Counts the number of empty cells within the list of arguments Excel Function: COUNTBLANK(value1[,value2[, ...]]) param: mixed ...$args Data values return: int |
| COUNTIF($aArgs, $condition) X-Ref |
| COUNTIF. Counts the number of cells that contain numbers within the list of arguments Excel Function: COUNTIF(value1[,value2[, ...]],condition) param: mixed $aArgs Data values param: string $condition the criteria that defines which cells will be counted return: int |
| COUNTIFS(...$args) X-Ref |
| 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 $args Criterias return: int |
| COVAR($yValues, $xValues) X-Ref |
| COVAR. Returns covariance, the average of the products of deviations for each data point pair. param: mixed $yValues array of mixed Data Series Y param: mixed $xValues array of mixed Data Series X return: float|string |
| CRITBINOM($trials, $probability, $alpha) X-Ref |
| 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 param: float $trials number of Bernoulli trials param: float $probability probability of a success on each trial param: float $alpha criterion value return: int|string |
| DEVSQ(...$args) X-Ref |
| DEVSQ. Returns the sum of squares of deviations of data points from their sample mean. Excel Function: DEVSQ(value1[,value2[, ...]]) param: mixed ...$args Data values return: float|string |
| EXPONDIST($value, $lambda, $cumulative) X-Ref |
| 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. param: float $value Value of the function param: float $lambda The parameter value param: bool $cumulative return: float|string |
| FISHER($value) X-Ref |
| 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. param: float $value return: float|string |
| FISHERINV($value) X-Ref |
| 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. param: float $value return: float|string |
| FORECAST($xValue, $yValues, $xValues) X-Ref |
| FORECAST. Calculates, or predicts, a future value by using existing values. The predicted value is a y-value for a given x-value. param: float $xValue Value of X for which we want to find Y param: mixed $yValues array of mixed Data Series Y param: mixed $xValues of mixed Data Series X return: bool|float|string |
| GAMMADIST($value, $a, $b, $cumulative) X-Ref |
| GAMMADIST. Returns the gamma distribution. param: float $value Value at which you want to evaluate the distribution param: float $a Parameter to the distribution param: float $b Parameter to the distribution param: bool $cumulative return: float|string |
| GAMMAINV($probability, $alpha, $beta) X-Ref |
| GAMMAINV. Returns the inverse of the beta distribution. param: float $probability Probability at which you want to evaluate the distribution param: float $alpha Parameter to the distribution param: float $beta Parameter to the distribution return: float|string |
| GAMMALN($value) X-Ref |
| GAMMALN. Returns the natural logarithm of the gamma function. param: float $value return: float|string |
| GEOMEAN(...$args) X-Ref |
| 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[, ...]]) param: mixed ...$args Data values return: float|string |
| GROWTH($yValues, $xValues = [], $newValues = [], $const = true) X-Ref |
| GROWTH. Returns values along a predicted exponential Trend param: mixed[] $yValues Data Series Y param: mixed[] $xValues Data Series X param: mixed[] $newValues Values of X for which we want to find Y param: bool $const a logical value specifying whether to force the intersect to equal 0 return: array of float |
| HARMEAN(...$args) X-Ref |
| 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[, ...]]) param: mixed ...$args Data values return: float|string |
| HYPGEOMDIST($sampleSuccesses, $sampleNumber, $populationSuccesses, $populationNumber) X-Ref |
| 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 $populationNumber Population size return: float|string |
| INTERCEPT($yValues, $xValues) X-Ref |
| INTERCEPT. Calculates the point at which a line will intersect the y-axis by using existing x-values and y-values. param: mixed[] $yValues Data Series Y param: mixed[] $xValues Data Series X return: float|string |
| KURT(...$args) X-Ref |
| 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. param: array ...$args Data Series return: float|string |
| LARGE(...$args) X-Ref |
| 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) param: mixed $args Data values param: int $entry Position (ordered from the largest) in the array or range of data to return return: float |
| LINEST($yValues, $xValues = null, $const = true, $stats = false) X-Ref |
| 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. param: mixed[] $yValues Data Series Y param: null|mixed[] $xValues Data Series X param: bool $const a logical value specifying whether to force the intersect to equal 0 param: bool $stats a logical value specifying whether to return additional regression statistics return: array |
| LOGEST($yValues, $xValues = null, $const = true, $stats = false) X-Ref |
| LOGEST. Calculates an exponential curve that best fits the X and Y data series, and then returns an array that describes the line. param: mixed[] $yValues Data Series Y param: null|mixed[] $xValues Data Series X param: bool $const a logical value specifying whether to force the intersect to equal 0 param: bool $stats a logical value specifying whether to return additional regression statistics return: array |
| LOGINV($probability, $mean, $stdDev) X-Ref |
| LOGINV. Returns the inverse of the normal cumulative distribution param: float $probability param: float $mean param: float $stdDev return: float |
| LOGNORMDIST($value, $mean, $stdDev) X-Ref |
| LOGNORMDIST. Returns the cumulative lognormal distribution of x, where ln(x) is normally distributed with parameters mean and standard_dev. param: float $value param: float $mean param: float $stdDev return: float |
| MAX(...$args) X-Ref |
| 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[, ...]]) param: mixed ...$args Data values return: float |
| MAXA(...$args) X-Ref |
| MAXA. Returns the greatest value in a list of arguments, including numbers, text, and logical values Excel Function: MAXA(value1[,value2[, ...]]) param: mixed ...$args Data values return: float |
| MAXIFS(...$args) X-Ref |
| 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], ...) param: mixed $args Data range and criterias return: float |
| MEDIAN(...$args) X-Ref |
| 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[, ...]]) param: mixed ...$args Data values return: float |
| MIN(...$args) X-Ref |
| 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[, ...]]) param: mixed ...$args Data values return: float |
| MINA(...$args) X-Ref |
| MINA. Returns the smallest value in a list of arguments, including numbers, text, and logical values Excel Function: MINA(value1[,value2[, ...]]) param: mixed ...$args Data values return: float |
| MINIFS(...$args) X-Ref |
| 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], ...) param: mixed $args Data range and criterias return: float |
| modeCalc($data) X-Ref |
| No description |
| MODE(...$args) X-Ref |
| MODE. Returns the most frequently occurring, or repetitive, value in an array or range of data Excel Function: MODE(value1[,value2[, ...]]) param: mixed ...$args Data values return: float |
| NEGBINOMDIST($failures, $successes, $probability) X-Ref |
| 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 $probability Probability of success on each trial return: float |
| NORMDIST($value, $mean, $stdDev, $cumulative) X-Ref |
| 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 $cumulative return: float |
| NORMINV($probability, $mean, $stdDev) X-Ref |
| 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 $stdDev Standard Deviation return: float |
| NORMSDIST($value) X-Ref |
| 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 $value return: float |
| NORMSINV($value) X-Ref |
| NORMSINV. Returns the inverse of the standard normal cumulative distribution param: float $value return: float |
| PERCENTILE(...$args) X-Ref |
| PERCENTILE. Returns the nth percentile of values in a range.. Excel Function: PERCENTILE(value1[,value2[, ...]],entry) param: mixed $args Data values param: float $entry Percentile value in the range 0..1, inclusive. return: float |
| PERCENTRANK($valueSet, $value, $significance = 3) X-Ref |
| 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 $significance the number of significant digits for the returned percentage value return: float |
| PERMUT($numObjs, $numInSet) X-Ref |
| 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. param: int $numObjs Number of different objects param: int $numInSet Number of objects in each permutation return: int|string Number of permutations |
| POISSON($value, $mean, $cumulative) X-Ref |
| 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 $cumulative return: float |
| QUARTILE(...$args) X-Ref |
| QUARTILE. Returns the quartile of a data set. Excel Function: QUARTILE(value1[,value2[, ...]],entry) param: mixed $args Data values param: int $entry Quartile value in the range 1..3, inclusive. return: float |
| RANK($value, $valueSet, $order = 0) X-Ref |
| 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 $order Order to sort the values in the value set return: float |
| RSQ($yValues, $xValues) X-Ref |
| RSQ. Returns the square of the Pearson product moment correlation coefficient through data points in known_y's and known_x's. param: mixed[] $yValues Data Series Y param: mixed[] $xValues Data Series X return: float|string |
| SKEW(...$args) X-Ref |
| 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. param: array ...$args Data Series return: float|string |
| SLOPE($yValues, $xValues) X-Ref |
| SLOPE. Returns the slope of the linear regression line through data points in known_y's and known_x's. param: mixed[] $yValues Data Series Y param: mixed[] $xValues Data Series X return: float|string |
| SMALL(...$args) X-Ref |
| 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) param: mixed $args Data values param: int $entry Position (ordered from the smallest) in the array or range of data to return return: float |
| STANDARDIZE($value, $mean, $stdDev) X-Ref |
| STANDARDIZE. Returns a normalized value from a distribution characterized by mean and standard_dev. param: float $value Value to normalize param: float $mean Mean Value param: float $stdDev Standard Deviation return: float Standardized value |
| STDEV(...$args) X-Ref |
| 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[, ...]]) param: mixed ...$args Data values return: float|string |
| STDEVA(...$args) X-Ref |
| STDEVA. Estimates standard deviation based on a sample, including numbers, text, and logical values Excel Function: STDEVA(value1[,value2[, ...]]) param: mixed ...$args Data values return: float|string |
| STDEVP(...$args) X-Ref |
| STDEVP. Calculates standard deviation based on the entire population Excel Function: STDEVP(value1[,value2[, ...]]) param: mixed ...$args Data values return: float|string |
| STDEVPA(...$args) X-Ref |
| STDEVPA. Calculates standard deviation based on the entire population, including numbers, text, and logical values Excel Function: STDEVPA(value1[,value2[, ...]]) param: mixed ...$args Data values return: float|string |
| STEYX($yValues, $xValues) X-Ref |
| STEYX. Returns the standard error of the predicted y-value for each x in the regression. param: mixed[] $yValues Data Series Y param: mixed[] $xValues Data Series X return: float|string |
| TDIST($value, $degrees, $tails) X-Ref |
| TDIST. Returns the probability of Student's T distribution. param: float $value Value for the function param: float $degrees degrees of freedom param: float $tails number of tails (1 or 2) return: float |
| TINV($probability, $degrees) X-Ref |
| TINV. Returns the one-tailed probability of the chi-squared distribution. param: float $probability Probability for the function param: float $degrees degrees of freedom return: float |
| TREND($yValues, $xValues = [], $newValues = [], $const = true) X-Ref |
| TREND. Returns values along a linear Trend param: mixed[] $yValues Data Series Y param: mixed[] $xValues Data Series X param: mixed[] $newValues Values of X for which we want to find Y param: bool $const a logical value specifying whether to force the intersect to equal 0 return: array of float |
| TRIMMEAN(...$args) X-Ref |
| 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) param: mixed $args Data values param: float $discard Percentage to discard return: float|string |
| VARFunc(...$args) X-Ref |
| VARFunc. Estimates variance based on a sample. Excel Function: VAR(value1[,value2[, ...]]) param: mixed ...$args Data values return: float |
| VARA(...$args) X-Ref |
| VARA. Estimates variance based on a sample, including numbers, text, and logical values Excel Function: VARA(value1[,value2[, ...]]) param: mixed ...$args Data values return: float |
| VARP(...$args) X-Ref |
| VARP. Calculates variance based on the entire population Excel Function: VARP(value1[,value2[, ...]]) param: mixed ...$args Data values return: float |
| VARPA(...$args) X-Ref |
| VARPA. Calculates variance based on the entire population, including numbers, text, and logical values Excel Function: VARPA(value1[,value2[, ...]]) param: mixed ...$args Data values return: float |
| WEIBULL($value, $alpha, $beta, $cumulative) X-Ref |
| WEIBULL. Returns the Weibull distribution. Use this distribution in reliability analysis, such as calculating a device's mean time to failure. param: float $value param: float $alpha Alpha Parameter param: float $beta Beta Parameter param: bool $cumulative return: float |
| ZTEST($dataSet, $m0, $sigma = null) X-Ref |
| ZTEST. Returns the Weibull distribution. Use this distribution in reliability analysis, such as calculating a device's mean time to failure. param: float $dataSet param: float $m0 Alpha Parameter param: float $sigma Beta Parameter return: float|string |
