Statistics/Chi-squared distribution: Difference between revisions

<math display="block"> x^s \, \Gamma(s) \, e^{-x} \sum_{m=0}^\infty\frac{x^m}{\Gamma(s+m+1)} </math>

and so, for the chi-squared cumulative probability distribution withand substituting chi-squaredsquare k, weinto have,s substitutingas k/2 and chi-squaresquared kx into sx as kx / 2,

: <math display="block"> F(x;\,k) = \frac{1}{\Gamma(kx/2)} x^{(k/2)} \, \Gamma(k/2) \, e^{-x/2} \sum_{m=0}^\infty\frac{(x/2)^m}{\Gamma(\frac{k}{2}+m+1)}. </math>

In practice, thisBecause series formulaformulas ismay oftenbe subject to accumulated errors from rounding in the frequently used region where x and k are under 10 and near one another., Youyou may therefore instead use a mathematics function library, if available for your programming task, to calculate gamma and incomplete gamma.

""" gamma CDF from lower incomplete gamma function,by usingseries MPFRformula library to get upper incompletewith gamma """

function gamma_cdf(ak, x)