Constants

LOG_GAMMA_X_MAX_VALUE

LOG_GAMMA_X_MAX_VALUE = 2.55E+305

XMININ

XMININ = 2.23E-308

EPS

EPS = 2.22E-16

MAX_VALUE

MAX_VALUE = 1.2E+308

MAX_ITERATIONS

MAX_ITERATIONS = 256

SQRT2PI

SQRT2PI = 2.5066282746310007

Properties

$logBetaCacheP

$logBetaCacheP : 

Type

$logBetaCacheQ

$logBetaCacheQ : 

Type

$logBetaCacheResult

$logBetaCacheResult : 

Type

$logGammaCacheResult

$logGammaCacheResult : 

Type

$logGammaCacheX

$logGammaCacheX : 

Type

Methods

AVEDEV()

AVEDEV(mixed  ...$args) : float

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[, ...]])

Parameters

mixed $args variadic

Data values

Returns

float

AVERAGE()

AVERAGE(mixed  ...$args) : float

AVERAGE.

Returns the average (arithmetic mean) of the arguments

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

Parameters

mixed $args variadic

Data values

Returns

float

AVERAGEA()

AVERAGEA(mixed  ...$args) : float

AVERAGEA.

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

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

Parameters

mixed $args variadic

Data values

Returns

float

AVERAGEIF()

AVERAGEIF(mixed  $aArgs, string  $condition, array<mixed,mixed>  $averageArgs = array()) : float

AVERAGEIF.

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

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

Parameters

mixed $aArgs

Data values

string $condition

the criteria that defines which cells will be checked

array<mixed,mixed> $averageArgs

Data values

Returns

float

BETADIST()

BETADIST(float  $value, float  $alpha, float  $beta, mixed  $rMin, mixed  $rMax = 1) : float

BETADIST.

Returns the beta distribution.

Parameters

float $value

Value at which you want to evaluate the distribution

float $alpha

Parameter to the distribution

float $beta

Parameter to the distribution

mixed $rMin
mixed $rMax

Returns

float

BETAINV()

BETAINV(float  $probability, float  $alpha, float  $beta, float  $rMin, float  $rMax = 1) : float

BETAINV.

Returns the inverse of the beta distribution.

Parameters

float $probability

Probability at which you want to evaluate the distribution

float $alpha

Parameter to the distribution

float $beta

Parameter to the distribution

float $rMin

Minimum value

float $rMax

Maximum value

Returns

float

BINOMDIST()

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

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.

Parameters

float $value

Number of successes in trials

float $trials

Number of trials

float $probability

Probability of success on each trial

boolean $cumulative

Returns

float

CHIDIST()

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

CHIDIST.

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

Parameters

float $value

Value for the function

float $degrees

degrees of freedom

Returns

float

CHIINV()

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

CHIINV.

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

Parameters

float $probability

Probability for the function

float $degrees

degrees of freedom

Returns

float

CONFIDENCE()

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

CONFIDENCE.

Returns the confidence interval for a population mean

Parameters

float $alpha
float $stdDev

Standard Deviation

float $size

Returns

float

CORREL()

CORREL(mixed  $yValues, null|mixed  $xValues = null) : float

CORREL.

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

Parameters

mixed $yValues

array of mixed Data Series Y

null|mixed $xValues

array of mixed Data Series X

Returns

float

COUNT()

COUNT(mixed  ...$args) : integer

COUNT.

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

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

Parameters

mixed $args variadic

Data values

Returns

integer

COUNTA()

COUNTA(mixed  ...$args) : integer

COUNTA.

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

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

Parameters

mixed $args variadic

Data values

Returns

integer

COUNTBLANK()

COUNTBLANK(mixed  ...$args) : integer

COUNTBLANK.

Counts the number of empty cells within the list of arguments

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

Parameters

mixed $args variadic

Data values

Returns

integer

COUNTIF()

COUNTIF(mixed  $aArgs, string  $condition) : integer

COUNTIF.

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

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

Parameters

mixed $aArgs

Data values

string $condition

the criteria that defines which cells will be counted

Returns

integer

COVAR()

COVAR(mixed  $yValues, mixed  $xValues) : float

COVAR.

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

Parameters

mixed $yValues

array of mixed Data Series Y

mixed $xValues

array of mixed Data Series X

Returns

float

CRITBINOM()

CRITBINOM(float  $trials, float  $probability, float  $alpha) : integer

CRITBINOM.

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

Parameters

float $trials

number of Bernoulli trials

float $probability

probability of a success on each trial

float $alpha

criterion value

Returns

integer

DEVSQ()

DEVSQ(mixed  ...$args) : float

DEVSQ.

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

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

Parameters

mixed $args variadic

Data values

Returns

float

EXPONDIST()

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

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.

Parameters

float $value

Value of the function

float $lambda

The parameter value

boolean $cumulative

Returns

float

FISHER()

FISHER(float  $value) : float

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.

Parameters

float $value

Returns

float

FISHERINV()

FISHERINV(float  $value) : float

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.

Parameters

float $value

Returns

float

FORECAST()

FORECAST(float  $xValue, mixed  $yValues, mixed  $xValues) : float

FORECAST.

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

Parameters

float $xValue

Value of X for which we want to find Y

mixed $yValues

array of mixed Data Series Y

mixed $xValues

of mixed Data Series X

Returns

float

GAMMADIST()

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

GAMMADIST.

Returns the gamma distribution.

Parameters

float $value

Value at which you want to evaluate the distribution

float $a

Parameter to the distribution

float $b

Parameter to the distribution

boolean $cumulative

Returns

float

GAMMAINV()

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

GAMMAINV.

Returns the inverse of the beta distribution.

Parameters

float $probability

Probability at which you want to evaluate the distribution

float $alpha

Parameter to the distribution

float $beta

Parameter to the distribution

Returns

float

GAMMALN()

GAMMALN(float  $value) : float

GAMMALN.

Returns the natural logarithm of the gamma function.

Parameters

float $value

Returns

float

GEOMEAN()

GEOMEAN(mixed  ...$args) : float

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[, ...]])

Parameters

mixed $args variadic

Data values

Returns

float

GROWTH()

GROWTH(array<mixed,mixed>  $yValues, array<mixed,mixed>  $xValues = array(), array<mixed,mixed>  $newValues = array(), boolean  $const = true) : array

GROWTH.

Returns values along a predicted emponential Trend

Parameters

array<mixed,mixed> $yValues

Data Series Y

array<mixed,mixed> $xValues

Data Series X

array<mixed,mixed> $newValues

Values of X for which we want to find Y

boolean $const

a logical value specifying whether to force the intersect to equal 0

Returns

array —

of float

HARMEAN()

HARMEAN(mixed  ...$args) : float

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[, ...]])

Parameters

mixed $args variadic

Data values

Returns

float

HYPGEOMDIST()

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

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.

Parameters

float $sampleSuccesses

Number of successes in the sample

float $sampleNumber

Size of the sample

float $populationSuccesses

Number of successes in the population

float $populationNumber

Population size

Returns

float

INTERCEPT()

INTERCEPT(array<mixed,mixed>  $yValues, array<mixed,mixed>  $xValues) : float

INTERCEPT.

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

Parameters

array<mixed,mixed> $yValues

Data Series Y

array<mixed,mixed> $xValues

Data Series X

Returns

float

KURT()

KURT(array  ...$args) : float

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.

Parameters

array $args variadic

Data Series

Returns

float

LARGE()

LARGE(mixed  $args) : float

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)

Parameters

mixed $args

Data values

Returns

float

LINEST()

LINEST(array<mixed,mixed>  $yValues, null|array<mixed,mixed>  $xValues = null, boolean  $const = true, boolean  $stats = false) : array

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.

Parameters

array<mixed,mixed> $yValues

Data Series Y

null|array<mixed,mixed> $xValues

Data Series X

boolean $const

a logical value specifying whether to force the intersect to equal 0

boolean $stats

a logical value specifying whether to return additional regression statistics

Returns

array

LOGEST()

LOGEST(array<mixed,mixed>  $yValues, null|array<mixed,mixed>  $xValues = null, boolean  $const = true, boolean  $stats = false) : array

LOGEST.

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

Parameters

array<mixed,mixed> $yValues

Data Series Y

null|array<mixed,mixed> $xValues

Data Series X

boolean $const

a logical value specifying whether to force the intersect to equal 0

boolean $stats

a logical value specifying whether to return additional regression statistics

Returns

array

LOGINV()

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

LOGINV.

Returns the inverse of the normal cumulative distribution

Parameters

float $probability
float $mean
float $stdDev

Returns

float

LOGNORMDIST()

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

LOGNORMDIST.

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

Parameters

float $value
float $mean
float $stdDev

Returns

float

MAX()

MAX(mixed  ...$args) : float

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[, ...]])

Parameters

mixed $args variadic

Data values

Returns

float

MAXA()

MAXA(mixed  ...$args) : float

MAXA.

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

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

Parameters

mixed $args variadic

Data values

Returns

float

MAXIF()

MAXIF(mixed  $aArgs, string  $condition, mixed  $sumArgs = array()) : float

MAXIF.

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

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

Parameters

mixed $aArgs

Data values

string $condition

the criteria that defines which cells will be checked

mixed $sumArgs

Returns

float

MEDIAN()

MEDIAN(mixed  ...$args) : float

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[, ...]])

Parameters

mixed $args variadic

Data values

Returns

float

MIN()

MIN(mixed  ...$args) : float

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[, ...]])

Parameters

mixed $args variadic

Data values

Returns

float

MINA()

MINA(mixed  ...$args) : float

MINA.

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

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

Parameters

mixed $args variadic

Data values

Returns

float

MINIF()

MINIF(mixed  $aArgs, string  $condition, mixed  $sumArgs = array()) : float

MINIF.

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

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

Parameters

mixed $aArgs

Data values

string $condition

the criteria that defines which cells will be checked

mixed $sumArgs

Returns

float

MODE()

MODE(mixed  ...$args) : float

MODE.

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

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

Parameters

mixed $args variadic

Data values

Returns

float

NEGBINOMDIST()

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

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.

Parameters

float $failures

Number of Failures

float $successes

Threshold number of Successes

float $probability

Probability of success on each trial

Returns

float

NORMDIST()

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

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.

Parameters

float $value
float $mean

Mean Value

float $stdDev

Standard Deviation

boolean $cumulative

Returns

float

NORMINV()

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

NORMINV.

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

Parameters

float $probability
float $mean

Mean Value

float $stdDev

Standard Deviation

Returns

float

NORMSDIST()

NORMSDIST(float  $value) : float

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.

Parameters

float $value

Returns

float

NORMSINV()

NORMSINV(float  $value) : float

NORMSINV.

Returns the inverse of the standard normal cumulative distribution

Parameters

float $value

Returns

float

PERCENTILE()

PERCENTILE(mixed  $args) : float

PERCENTILE.

Returns the nth percentile of values in a range..

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

Parameters

mixed $args

Data values

Returns

float

PERCENTRANK()

PERCENTRANK(array<mixed,float>  $valueSet, integer  $value, integer  $significance = 3) : float

PERCENTRANK.

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

Parameters

array<mixed,float> $valueSet

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

integer $value

the number whose rank you want to find

integer $significance

the number of significant digits for the returned percentage value

Returns

float

PERMUT()

PERMUT(integer  $numObjs, integer  $numInSet) : integer

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.

Parameters

integer $numObjs

Number of different objects

integer $numInSet

Number of objects in each permutation

Returns

integer —

Number of permutations

POISSON()

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

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.

Parameters

float $value
float $mean

Mean Value

boolean $cumulative

Returns

float

QUARTILE()

QUARTILE(mixed  $args) : float

QUARTILE.

Returns the quartile of a data set.

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

Parameters

mixed $args

Data values

Returns

float

RANK()

RANK(integer  $value, array<mixed,float>  $valueSet, integer  $order) : float

RANK.

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

Parameters

integer $value

the number whose rank you want to find

array<mixed,float> $valueSet

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

integer $order

Order to sort the values in the value set

Returns

float

RSQ()

RSQ(array<mixed,mixed>  $yValues, array<mixed,mixed>  $xValues) : float

RSQ.

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

Parameters

array<mixed,mixed> $yValues

Data Series Y

array<mixed,mixed> $xValues

Data Series X

Returns

float

SKEW()

SKEW(array  ...$args) : float

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.

Parameters

array $args variadic

Data Series

Returns

float

SLOPE()

SLOPE(array<mixed,mixed>  $yValues, array<mixed,mixed>  $xValues) : float

SLOPE.

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

Parameters

array<mixed,mixed> $yValues

Data Series Y

array<mixed,mixed> $xValues

Data Series X

Returns

float

SMALL()

SMALL(mixed  $args) : float

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)

Parameters

mixed $args

Data values

Returns

float

STANDARDIZE()

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

STANDARDIZE.

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

Parameters

float $value

Value to normalize

float $mean

Mean Value

float $stdDev

Standard Deviation

Returns

float —

Standardized value

STDEV()

STDEV(mixed  ...$args) : float

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[, ...]])

Parameters

mixed $args variadic

Data values

Returns

float

STDEVA()

STDEVA(mixed  ...$args) : float

STDEVA.

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

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

Parameters

mixed $args variadic

Data values

Returns

float

STDEVP()

STDEVP(mixed  ...$args) : float

STDEVP.

Calculates standard deviation based on the entire population

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

Parameters

mixed $args variadic

Data values

Returns

float

STDEVPA()

STDEVPA(mixed  ...$args) : float

STDEVPA.

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

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

Parameters

mixed $args variadic

Data values

Returns

float

STEYX()

STEYX(array<mixed,mixed>  $yValues, array<mixed,mixed>  $xValues) : float

STEYX.

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

Parameters

array<mixed,mixed> $yValues

Data Series Y

array<mixed,mixed> $xValues

Data Series X

Returns

float

TDIST()

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

TDIST.

Returns the probability of Student's T distribution.

Parameters

float $value

Value for the function

float $degrees

degrees of freedom

float $tails

number of tails (1 or 2)

Returns

float

TINV()

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

TINV.

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

Parameters

float $probability

Probability for the function

float $degrees

degrees of freedom

Returns

float

TREND()

TREND(array<mixed,mixed>  $yValues, array<mixed,mixed>  $xValues = array(), array<mixed,mixed>  $newValues = array(), boolean  $const = true) : array

TREND.

Returns values along a linear Trend

Parameters

array<mixed,mixed> $yValues

Data Series Y

array<mixed,mixed> $xValues

Data Series X

array<mixed,mixed> $newValues

Values of X for which we want to find Y

boolean $const

a logical value specifying whether to force the intersect to equal 0

Returns

array —

of float

TRIMMEAN()

TRIMMEAN(mixed  $args) : float

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)

Parameters

mixed $args

Data values

Returns

float

VARFunc()

VARFunc(mixed  ...$args) : float

VARFunc.

Estimates variance based on a sample.

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

Parameters

mixed $args variadic

Data values

Returns

float

VARA()

VARA(mixed  ...$args) : float

VARA.

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

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

Parameters

mixed $args variadic

Data values

Returns

float

VARP()

VARP(mixed  ...$args) : float

VARP.

Calculates variance based on the entire population

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

Parameters

mixed $args variadic

Data values

Returns

float

VARPA()

VARPA(mixed  ...$args) : float

VARPA.

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

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

Parameters

mixed $args variadic

Data values

Returns

float

WEIBULL()

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

WEIBULL.

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

Parameters

float $value
float $alpha

Alpha Parameter

float $beta

Beta Parameter

boolean $cumulative

Returns

float

ZTEST()

ZTEST(float  $dataSet, float  $m0, float  $sigma = null) : float

ZTEST.

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

Parameters

float $dataSet
float $m0

Alpha Parameter

float $sigma

Beta Parameter

Returns

float

checkTrendArrays()

checkTrendArrays(  $array1,   $array2) 

Parameters

$array1
$array2

incompleteBeta()

incompleteBeta(mixed  $x, mixed  $p, mixed  $q) : float

Incomplete beta function.

Parameters

mixed $x

require 0<=x<=1

mixed $p

require p>0

mixed $q

require q>0

Returns

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()

logBeta(mixed  $p, mixed  $q) : float

The natural logarithm of the beta function.

Parameters

mixed $p

require p>0

mixed $q

require q>0

Returns

float —

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

betaFraction()

betaFraction(mixed  $x, mixed  $p, mixed  $q) : float

Evaluates of continued fraction part of incomplete beta function.

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

Parameters

mixed $x
mixed $p
mixed $q

Returns

float

logGamma()

logGamma(  $x) 

Parameters

$x

incompleteGamma()

incompleteGamma(  $a,   $x) 

Parameters

$a
$x

gamma()

gamma(  $data) 

Parameters

$data

inverseNcdf()

inverseNcdf(  $p) 

Parameters

$p

modeCalc()

modeCalc(  $data) 

Parameters

$data