# 3.5.3.1.16 Ncchi2cdf

## Definition:

$prob = ncchi2cdf(x, f, lambda)$ computes the probability associated with the lower tail of the non-central $\chi^2$ distribution.

The lower tail probability of the non-central $\chi^2$ distribution with $\nu$ degrees of freedom and non-centrality parameter $\lambda$ , $P(X\le x:\nu; \lambda)$is defined by:
$P(X\le x: \nu;\lambda)=\sum_{j=0}^\infty {e^{-\frac{\lambda}{2}}\frac{{(\lambda/2)}^j}{j!}P(X\le x:\nu+2j;0)}$.
where $P(X\le x:\nu+2j;0)$ is a central $\chi^2$ with $\nu+ 2j$ degrees of freedom.

## Parameters:

x (input,double)
The deviation from the non-central $\chi^2$ distribution with $\nu$ degrees of freedom and non-centrality parameter $\lambda$ . $x \ge 0$.
f (input,double)
The degrees of freedom, $\nu$ , of the non-central $\chi^2$ distribution. $f\ge 0$ .
lambda (input,double)
The non-centrality parameter, $\lambda$ , of the non-central $\chi^2$ distribution. lambda > 0 if $f= 0$; lambda $\ge 0$ if $f > 0$ .
prob (output,double)
The probability.