3.5.3.2.16 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.