# 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,$x_p$.