Chi-Squared (non-central)

Parameters

Degrees of freedom (\(\nu \)) and non-centrality parameter (\(\delta\)). \(\nu \) must be integer and \(\delta\) must be non-negative.

Support

\(\left[ 0,\infty \right) \)

Mean

\(\nu + \delta \)

Variance

\(2\nu  + 4\delta \)

Main Uses

Asymptotic distribution and approximate distributions for certain non-standard testing procedures.

Density Function

%CHISQRNCDENSITY(x,nu,delta) is the (non-logged) density with parameters nu and delta at x.

CDF

%CHISQRNC(x,nu,delta) is the CDF, not the tail probability.

Inverse CDF

%INVCHISQRNC(p,nu,delta) returns the x value given parameters nu and delta which gives a CDF of p.