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  •  JAMA Pythagorean Theorem: a = 3 b = 4 r = sqrt(square(a) + square(b)) r = 5 r = sqrt(a^2 + b^2) without under/overflow
  •  PHPExcel
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    PHPExcel_Calculation_Statistical

    category PHPExcel
    package PHPExcel_Calculation
    copyright Copyright (c) 2006 - 2014 PHPExcel (http://www.codeplex.com/PHPExcel)

     Methods

    AVEDEV

    AVEDEV() : float
    Static

    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[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    AVERAGE

    AVERAGE() : float
    Static

    Returns the average (arithmetic mean) of the arguments

    Excel Function: AVERAGE(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    AVERAGEA

    AVERAGEA() : float
    Static

    Returns the average of its arguments, including numbers, text, and logical values

    Excel Function: AVERAGEA(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    AVERAGEIF

    AVERAGEIF($aArgs, string $condition, mixed[] $averageArgs) : float
    Static

    Returns the average value from a range of cells that contain numbers within the list of arguments

    Excel Function: AVERAGEIF(value1[,value2[, ...]],condition)

    access public
    category Mathematical and Trigonometric Functions

    Parameters

    $aArgs

    $condition

    string

    The criteria that defines which cells will be checked.

    $averageArgs

    mixed[]

    Data values

    Returns

    float

    BETADIST

    BETADIST(float $value, float $alpha, float $beta, $rMin, $rMax) : float
    Static

    Returns the beta distribution.

    Parameters

    $value

    float

    Value at which you want to evaluate the distribution

    $alpha

    float

    Parameter to the distribution

    $beta

    float

    Parameter to the distribution

    $rMin

    $rMax

    Returns

    float

    BETAINV

    BETAINV(float $probability, float $alpha, float $beta, float $rMin, float $rMax) : float
    Static

    Returns the inverse of the beta distribution.

    Parameters

    $probability

    float

    Probability at which you want to evaluate the distribution

    $alpha

    float

    Parameter to the distribution

    $beta

    float

    Parameter to the distribution

    $rMin

    float

    Minimum value

    $rMax

    float

    Maximum value

    Returns

    float

    BINOMDIST

    BINOMDIST(float $value, float $trials, float $probability, boolean $cumulative) : float
    Static

    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.

    todo Cumulative distribution function

    Parameters

    $value

    float

    Number of successes in trials

    $trials

    float

    Number of trials

    $probability

    float

    Probability of success on each trial

    $cumulative

    boolean

    Returns

    float

    CHIDIST

    CHIDIST(float $value, float $degrees) : float
    Static

    Returns the one-tailed probability of the chi-squared distribution.

    Parameters

    $value

    float

    Value for the function

    $degrees

    float

    degrees of freedom

    Returns

    float

    CHIINV

    CHIINV(float $probability, float $degrees) : float
    Static

    Returns the one-tailed probability of the chi-squared distribution.

    Parameters

    $probability

    float

    Probability for the function

    $degrees

    float

    degrees of freedom

    Returns

    float

    CONFIDENCE

    CONFIDENCE(float $alpha, float $stdDev, float $size) : float
    Static

    Returns the confidence interval for a population mean

    Parameters

    $alpha

    float

    $stdDev

    float

    Standard Deviation

    $size

    float

    Returns

    float

    CORREL

    CORREL(array $yValues, array $xValues) : float
    Static

    Returns covariance, the average of the products of deviations for each data point pair.

    Parameters

    $yValues

    array

    of mixed Data Series Y

    $xValues

    array

    of mixed Data Series X

    Returns

    float

    COUNT

    COUNT() : int
    Static

    Counts the number of cells that contain numbers within the list of arguments

    Excel Function: COUNT(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    int

    COUNTA

    COUNTA() : int
    Static

    Counts the number of cells that are not empty within the list of arguments

    Excel Function: COUNTA(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    int

    COUNTBLANK

    COUNTBLANK() : int
    Static

    Counts the number of empty cells within the list of arguments

    Excel Function: COUNTBLANK(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    int

    COUNTIF

    COUNTIF($aArgs, string $condition) : int
    Static

    Counts the number of cells that contain numbers within the list of arguments

    Excel Function: COUNTIF(value1[,value2[, ...]],condition)

    access public
    category Statistical Functions

    Parameters

    $aArgs

    $condition

    string

    The criteria that defines which cells will be counted.

    Returns

    int

    COVAR

    COVAR(array $yValues, array $xValues) : float
    Static

    Returns covariance, the average of the products of deviations for each data point pair.

    Parameters

    $yValues

    array

    of mixed Data Series Y

    $xValues

    array

    of mixed Data Series X

    Returns

    float

    CRITBINOM

    CRITBINOM(float $trials, float $probability, float $alpha) : int
    Static

    Returns the smallest value for which the cumulative binomial distribution is greater than or equal to a criterion value

    See http://support.microsoft.com/kb/828117/ for details of the algorithm used

    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).

    Parameters

    $trials

    float

    number of Bernoulli trials

    $probability

    float

    probability of a success on each trial

    $alpha

    float

    criterion value

    Returns

    int

    DEVSQ

    DEVSQ() : float
    Static

    Returns the sum of squares of deviations of data points from their sample mean.

    Excel Function: DEVSQ(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    EXPONDIST

    EXPONDIST(float $value, float $lambda, boolean $cumulative) : float
    Static

    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.

    Parameters

    $value

    float

    Value of the function

    $lambda

    float

    The parameter value

    $cumulative

    boolean

    Returns

    float

    FISHER

    FISHER(float $value) : float
    Static

    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.

    Parameters

    $value

    float

    Returns

    float

    FISHERINV

    FISHERINV(float $value) : float
    Static

    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.

    Parameters

    $value

    float

    Returns

    float

    FORECAST

    FORECAST(float $xValue, array $yValues, array $xValues) : float
    Static

    Calculates, or predicts, a future value by using existing values. The predicted value is a y-value for a given x-value.

    Parameters

    $xValue

    float

    Value of X for which we want to find Y

    $yValues

    array

    of mixed Data Series Y

    $xValues

    array

    of mixed Data Series X

    Returns

    float

    GAMMADIST

    GAMMADIST(float $value, float $a, float $b, boolean $cumulative) : float
    Static

    Returns the gamma distribution.

    Parameters

    $value

    float

    Value at which you want to evaluate the distribution

    $a

    float

    Parameter to the distribution

    $b

    float

    Parameter to the distribution

    $cumulative

    boolean

    Returns

    float

    GAMMAINV

    GAMMAINV(float $probability, float $alpha, float $beta) : float
    Static

    Returns the inverse of the beta distribution.

    Parameters

    $probability

    float

    Probability at which you want to evaluate the distribution

    $alpha

    float

    Parameter to the distribution

    $beta

    float

    Parameter to the distribution

    Returns

    float

    GAMMALN

    GAMMALN(float $value) : float
    Static

    Returns the natural logarithm of the gamma function.

    Parameters

    $value

    float

    Returns

    float

    GEOMEAN

    GEOMEAN() : float
    Static

    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[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    GROWTH

    GROWTH(array $yValues, array $xValues, array $newValues, boolean $const) : array
    Static

    Returns values along a predicted emponential trend

    Parameters

    $yValues

    array

    of mixed Data Series Y

    $xValues

    array

    of mixed Data Series X

    $newValues

    array

    of mixed Values of X for which we want to find Y

    $const

    boolean

    A logical value specifying whether to force the intersect to equal 0.

    Returns

    arrayof float

    HARMEAN

    HARMEAN() : float
    Static

    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[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    HYPGEOMDIST

    HYPGEOMDIST(float $sampleSuccesses, float $sampleNumber, float $populationSuccesses, float $populationNumber) : float
    Static

    Returns the hypergeometric distribution. HYPGEOMDIST returns the probability of a given number of sample successes, given the sample size, population successes, and population size.

    Parameters

    $sampleSuccesses

    float

    Number of successes in the sample

    $sampleNumber

    float

    Size of the sample

    $populationSuccesses

    float

    Number of successes in the population

    $populationNumber

    float

    Population size

    Returns

    float

    INTERCEPT

    INTERCEPT(array $yValues, array $xValues) : float
    Static

    Calculates the point at which a line will intersect the y-axis by using existing x-values and y-values.

    Parameters

    $yValues

    array

    of mixed Data Series Y

    $xValues

    array

    of mixed Data Series X

    Returns

    float

    KURT

    KURT() : float
    Static

    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.

    Returns

    float

    LARGE

    LARGE() : float
    Static

    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)

    access public
    category Statistical Functions

    Returns

    float

    LINEST

    LINEST(array $yValues, array $xValues, boolean $const, boolean $stats) : array
    Static

    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.

    Parameters

    $yValues

    array

    of mixed Data Series Y

    $xValues

    array

    of mixed Data Series X

    $const

    boolean

    A logical value specifying whether to force the intersect to equal 0.

    $stats

    boolean

    A logical value specifying whether to return additional regression statistics.

    Returns

    array

    LOGEST

    LOGEST(array $yValues, array $xValues, boolean $const, boolean $stats) : array
    Static

    Calculates an exponential curve that best fits the X and Y data series, and then returns an array that describes the line.

    Parameters

    $yValues

    array

    of mixed Data Series Y

    $xValues

    array

    of mixed Data Series X

    $const

    boolean

    A logical value specifying whether to force the intersect to equal 0.

    $stats

    boolean

    A logical value specifying whether to return additional regression statistics.

    Returns

    array

    LOGINV

    LOGINV(float $probability, float $mean, float $stdDev) : float
    Static

    Returns the inverse of the normal cumulative distribution

    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/

    Parameters

    $probability

    float

    $mean

    float

    $stdDev

    float

    Returns

    float

    LOGNORMDIST

    LOGNORMDIST(float $value, float $mean, float $stdDev) : float
    Static

    Returns the cumulative lognormal distribution of x, where ln(x) is normally distributed with parameters mean and standard_dev.

    Parameters

    $value

    float

    $mean

    float

    $stdDev

    float

    Returns

    float

    MAX

    MAX() : float
    Static

    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[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    MAXA

    MAXA() : float
    Static

    Returns the greatest value in a list of arguments, including numbers, text, and logical values

    Excel Function: MAXA(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    MAXIF

    MAXIF($aArgs, string $condition, $sumArgs) : float
    Static

    Counts the maximum value within a range of cells that contain numbers within the list of arguments

    Excel Function: MAXIF(value1[,value2[, ...]],condition)

    access public
    category Mathematical and Trigonometric Functions

    Parameters

    $aArgs

    $condition

    string

    The criteria that defines which cells will be checked.

    $sumArgs

    Returns

    float

    MEDIAN

    MEDIAN() : float
    Static

    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[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    MIN

    MIN() : float
    Static

    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[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    MINA

    MINA() : float
    Static

    Returns the smallest value in a list of arguments, including numbers, text, and logical values

    Excel Function: MINA(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    MINIF

    MINIF($aArgs, string $condition, $sumArgs) : float
    Static

    Returns the minimum value within a range of cells that contain numbers within the list of arguments

    Excel Function: MINIF(value1[,value2[, ...]],condition)

    access public
    category Mathematical and Trigonometric Functions

    Parameters

    $aArgs

    $condition

    string

    The criteria that defines which cells will be checked.

    $sumArgs

    Returns

    float

    MODE

    MODE() : float
    Static

    Returns the most frequently occurring, or repetitive, value in an array or range of data

    Excel Function: MODE(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    NEGBINOMDIST

    NEGBINOMDIST(float $failures, float $successes, float $probability) : float
    Static

    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.

    Parameters

    $failures

    float

    Number of Failures

    $successes

    float

    Threshold number of Successes

    $probability

    float

    Probability of success on each trial

    Returns

    float

    NORMDIST

    NORMDIST(float $value, float $mean, float $stdDev, boolean $cumulative) : float
    Static

    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.

    Parameters

    $value

    float

    $mean

    float

    Mean Value

    $stdDev

    float

    Standard Deviation

    $cumulative

    boolean

    Returns

    float

    NORMINV

    NORMINV($probability, float $mean, float $stdDev) : float
    Static

    Returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.

    Parameters

    $probability

    $mean

    float

    Mean Value

    $stdDev

    float

    Standard Deviation

    Returns

    float

    NORMSDIST

    NORMSDIST(float $value) : float
    Static

    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.

    Parameters

    $value

    float

    Returns

    float

    NORMSINV

    NORMSINV(float $value) : float
    Static

    Returns the inverse of the standard normal cumulative distribution

    Parameters

    $value

    float

    Returns

    float

    PERCENTILE

    PERCENTILE() : float
    Static

    Returns the nth percentile of values in a range..

    Excel Function: PERCENTILE(value1[,value2[, ...]],entry)

    access public
    category Statistical Functions

    Returns

    float

    PERCENTRANK

    PERCENTRANK(array $valueSet, \number $value, \number $significance) : float
    Static

    Returns the rank of a value in a data set as a percentage of the data set.

    Parameters

    $valueSet

    array

    of number An array of, or a reference to, a list of numbers.

    $value

    \number

    The number whose rank you want to find.

    $significance

    \number

    The number of significant digits for the returned percentage value.

    Returns

    float

    PERMUT

    PERMUT(int $numObjs, int $numInSet) : int
    Static

    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.

    Parameters

    $numObjs

    int

    Number of different objects

    $numInSet

    int

    Number of objects in each permutation

    Returns

    intNumber of permutations

    POISSON

    POISSON(float $value, float $mean, boolean $cumulative) : float
    Static

    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.

    Parameters

    $value

    float

    $mean

    float

    Mean Value

    $cumulative

    boolean

    Returns

    float

    QUARTILE

    QUARTILE() : float
    Static

    Returns the quartile of a data set.

    Excel Function: QUARTILE(value1[,value2[, ...]],entry)

    access public
    category Statistical Functions

    Returns

    float

    RANK

    RANK(\number $value, array $valueSet, mixed $order) : float
    Static

    Returns the rank of a number in a list of numbers.

    Parameters

    $value

    \number

    The number whose rank you want to find.

    $valueSet

    array

    of number An array of, or a reference to, a list of numbers.

    $order

    mixed

    Order to sort the values in the value set

    Returns

    float

    RSQ

    RSQ(array $yValues, array $xValues) : float
    Static

    Returns the square of the Pearson product moment correlation coefficient through data points in known_y's and known_x's.

    Parameters

    $yValues

    array

    of mixed Data Series Y

    $xValues

    array

    of mixed Data Series X

    Returns

    float

    SKEW

    SKEW() : float
    Static

    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.

    Returns

    float

    SLOPE

    SLOPE(array $yValues, array $xValues) : float
    Static

    Returns the slope of the linear regression line through data points in known_y's and known_x's.

    Parameters

    $yValues

    array

    of mixed Data Series Y

    $xValues

    array

    of mixed Data Series X

    Returns

    float

    SMALL

    SMALL() : float
    Static

    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)

    access public
    category Statistical Functions

    Returns

    float

    STANDARDIZE

    STANDARDIZE(float $value, float $mean, float $stdDev) : float
    Static

    Returns a normalized value from a distribution characterized by mean and standard_dev.

    Parameters

    $value

    float

    Value to normalize

    $mean

    float

    Mean Value

    $stdDev

    float

    Standard Deviation

    Returns

    floatStandardized value

    STDEV

    STDEV() : float
    Static

    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[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    STDEVA

    STDEVA() : float
    Static

    Estimates standard deviation based on a sample, including numbers, text, and logical values

    Excel Function: STDEVA(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    STDEVP

    STDEVP() : float
    Static

    Calculates standard deviation based on the entire population

    Excel Function: STDEVP(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    STDEVPA

    STDEVPA() : float
    Static

    Calculates standard deviation based on the entire population, including numbers, text, and logical values

    Excel Function: STDEVPA(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    STEYX

    STEYX(array $yValues, array $xValues) : float
    Static

    Returns the standard error of the predicted y-value for each x in the regression.

    Parameters

    $yValues

    array

    of mixed Data Series Y

    $xValues

    array

    of mixed Data Series X

    Returns

    float

    TDIST

    TDIST(float $value, float $degrees, float $tails) : float
    Static

    Returns the probability of Student's T distribution.

    Parameters

    $value

    float

    Value for the function

    $degrees

    float

    degrees of freedom

    $tails

    float

    number of tails (1 or 2)

    Returns

    float

    TINV

    TINV(float $probability, float $degrees) : float
    Static

    Returns the one-tailed probability of the chi-squared distribution.

    Parameters

    $probability

    float

    Probability for the function

    $degrees

    float

    degrees of freedom

    Returns

    float

    TREND

    TREND(array $yValues, array $xValues, array $newValues, boolean $const) : array
    Static

    Returns values along a linear trend

    Parameters

    $yValues

    array

    of mixed Data Series Y

    $xValues

    array

    of mixed Data Series X

    $newValues

    array

    of mixed Values of X for which we want to find Y

    $const

    boolean

    A logical value specifying whether to force the intersect to equal 0.

    Returns

    arrayof float

    TRIMMEAN

    TRIMMEAN() : float
    Static

    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)

    access public
    category Statistical Functions

    Returns

    float

    VARA

    VARA() : float
    Static

    Estimates variance based on a sample, including numbers, text, and logical values

    Excel Function: VARA(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    VARFunc

    VARFunc() : float
    Static

    Estimates variance based on a sample.

    Excel Function: VAR(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    VARP

    VARP() : float
    Static

    Calculates variance based on the entire population

    Excel Function: VARP(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    VARPA

    VARPA() : float
    Static

    Calculates variance based on the entire population, including numbers, text, and logical values

    Excel Function: VARPA(value1[,value2[, ...]])

    access public
    category Statistical Functions

    Returns

    float

    WEIBULL

    WEIBULL(float $value, float $alpha, float $beta, boolean $cumulative) : float
    Static

    Returns the Weibull distribution. Use this distribution in reliability analysis, such as calculating a device's mean time to failure.

    Parameters

    $value

    float

    $alpha

    float

    Alpha Parameter

    $beta

    float

    Beta Parameter

    $cumulative

    boolean

    Returns

    float

    ZTEST

    ZTEST(float $dataSet, float $m0, float $sigma) : float
    Static

    Returns the Weibull distribution. Use this distribution in reliability analysis, such as calculating a device's mean time to failure.

    Parameters

    $dataSet

    float

    $m0

    float

    Alpha Parameter

    $sigma

    float

    Beta Parameter

    Returns

    float

    Beta function.

    _beta(\p $p, \q $q) : 
    Static
    author Jaco van Kooten

    Parameters

    $p

    \p

    require p>0

    $q

    \q

    require q>0

    Returns

    if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow

    Evaluates of continued fraction part of incomplete beta function.

    _betaFraction($x, $p, $q) 
    Static

    Based on an idea from Numerical Recipes (W.H. Press et al, 1992).

    author Jaco van Kooten

    Parameters

    $x

    $p

    $q

    _checkTrendArrays() 

    _checkTrendArrays($array1, $array2) 
    Static

    Parameters

    $array1

    $array2

    _gamma() 

    _gamma($data) 
    Static

    Parameters

    $data

    Incomplete beta function

    _incompleteBeta(\x $x, \p $p, \q $q) : 
    Static
    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).

    Parameters

    $x

    \x

    require 0<=x<=1

    $p

    \p

    require p>0

    $q

    \q

    require q>0

    Returns

    if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow

    _incompleteGamma() 

    _incompleteGamma($a, $x) 
    Static

    Parameters

    $a

    $x

    _inverse_ncdf() 

    _inverse_ncdf($p) 
    Static

    Parameters

    $p

    _inverse_ncdf2() 

    _inverse_ncdf2($prob) 
    Static

    Parameters

    $prob

    _inverse_ncdf3() 

    _inverse_ncdf3($p) 
    Static

    Parameters

    $p

    The natural logarithm of the beta function.

    _logBeta(\p $p, \q $q) : 
    Static
    author Jaco van Kooten

    Parameters

    $p

    \p

    require p>0

    $q

    \q

    require q>0

    Returns

    if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow

    _logGamma() 

    _logGamma($x) 
    Static

    Parameters

    $x

    _modeCalc() 

    _modeCalc($data) 
    Static

    Parameters

    $data

     Properties

     

    $_logBetaCache_p 
     

    $_logBetaCache_q 
     

    $_logBetaCache_result 
     

    $_logGammaCache_result 
     

    $_logGammaCache_x