3.5.3.3.2 Chi2inv

Definition:

\(xp = chi2inv( p, df)\) computes the inverse of the \(\chi^2\) cdf for the corresponding probabilities in \(X\) with parameters specified by \(\nu\).

The deviate,\(x_p\), associated with the lower tail probability \(p\) of the \(\chi^2\) distribution with degrees of freedom is defined as the solution to

\[ P(X\leq x_p)=p=\frac 1{2^{\nu /2}\Gamma (\nu /2)}\int_0^{x_p}X^{\nu /2-1}e^{X/2}dX \]

where

\[ x_p\geq 0;\nu >0 \]

Parameters:

\(p\) (input, double)

the probability, \(p\), from the required \(\chi^2\) distribution. \(0 \le p<1\)

\(df\) (input,double)

the degrees of freedom, \(\nu\) , of the \(\chi^2\) distribution, \(df>0\).

\(xp\) (output, double)

the deviate,\(x_p\).