Chi-square distribution with *k* degrees of freedom is a distribution of the sum of squares of *k* random variables having normal distribution with mean equal to 0 and standard deviation equal to 1.

Probability density function for chi-square distribution is:

Cumulative distribution function of the the chi-square distribution is:

**ChiSquareDistribution** and **ChiSquareCDistribution** subroutines are used to calculate the areas under the left and right tails of the graph (i.e. to calculate cumulative distribution function and its own complement). **InvChiSquareCDistribution** subroutine calculates the inverse cumulative distribution function. Subroutines use the above mentioned formula which calculates cumulative distribution function by using an incomplete gamma-function.

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