3.5.3.1.19 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.