## 15.8 Using Statistical Functions

The following statistical functions are supported in this release:

Function Name Description

`beta1(value1,value2,value3)`

Returns the area from zero to `value3` under the beta density function

`betaComplemented(value1,value2,value3)`

Returns the area under the right hand tail (from `value3` to infinity) of the beta density function

`binomial2(value1,value2,value3)`

Returns the sum of the terms 0 through `value1` of the Binomial probability density. All arguments must be positive.

`binomialComplemented(value1,value2,value3)`

Returns the sum of the terms `value1+1` through `value2` of the binomial probability density. All arguments must be positive.

`chiSquare(value1,value2)`

Returns the area under the left hand tail (from 0 to `value2`) of the chi square probability density function with `value1` degrees of freedom. The arguments must both be positive.

`chiSquareComplemented(value1,value2)`

Returns the area under the right hand tail (from `value2` to infinity) of the chi square probability density function with `value1` degrees of freedom. The arguments must both be positive.

`errorFunction(value1)`

Returns the error function of the normal distribution

`errorFunctionComplemented(value1)`

Returns the complementary error function of the normal distribution

`gamma(value1,value2,value3)`

Returns the gamma function of the arguments

`gammaComplemented(value1,value2,value3)`

Returns the integral from `value3` to infinity of the gamma probability density function

`incompleteBeta(value1,value2,value3)`

Returns the incomplete beta function evaluated from zero to `value3`

`incompleteGamma(value1,value2)`

Returns the incomplete gamma function

`incompleteGammaComplement(value1,value2)`

Returns the complemented incomplete gamma function

`logGamma(value1)`

Returns the natural logarithm of the gamma function

`negativeBinomial(value1,value2,value3)`

Returns the sum of the terms 0 through `value1` of the negative binomial distribution. All arguments must be positive.

`negativeBinomialComplemented(value1,value2,value3)`

Returns the sum of the terms `value1+1` to infinity of the negative binomial distribution. All arguments must be positive.

`normal(value1,value2,value3)`

Returns the area under the normal (Gaussian) probability density function, integrated from minus infinity to `value1` (assumes mean is zero, variance is one)

`normalInverse(value1)`

Returns the value for which the area under the normal (Gaussian) probability density function is equal to the argument `value1` (assumes mean is zero, variance is one)

`poisson(value1,value2)`

Returns the sum of the first `value1` terms of the Poisson distribution. The arguments must both be positive.

`poissonComplemented(value1,value2)`

Returns the sum of the terms `value1+1` to infinity of the poisson distribution

`studentT(value1,value2)`

Returns the integral from minus infinity to `value2` of the Student-t distribution with `value1` > 0 degrees of freedom

`studentTInverse(value1,value2)`

Returns the value, for which the area under the Student-t probability density function is equal to `1-value1/2`. The function uses the studentT function to determine the return value iteratively.