Noncentral chi-square cumulative distribution function
p = ncx2cdf(x,v,delta)
p = ncx2cdf(x,v,delta,'upper')
p = ncx2cdf(x,v,delta) computes the noncentral chi-square cdf at each value in x using the corresponding degrees of freedom in v and positive noncentrality parameters in delta. x, v, and delta can be vectors, matrices, or multidimensional arrays that all have the same size, which is also the size of p. A scalar input for x, v, or delta is expanded to a constant array with the same dimensions as the other inputs.
p = ncx2cdf(x,v,delta,'upper') returns the complement of the noncentral chi-square cdf at each value in x, using an algorithm that more accurately computes the extreme upper tail probabilities.
Some texts refer to this distribution as the generalized Rayleigh, Rayleigh-Rice, or Rice distribution.
The noncentral chi-square cdf is
Compare the noncentral chi-square cdf with DELTA = 2 to the chi-square cdf with the same number of degrees of freedom (4):
x = (0:0.1:10)'; ncx2 = ncx2cdf(x,4,2); chi2 = chi2cdf(x,4); plot(x,ncx2,'b-','LineWidth',2) hold on plot(x,chi2,'g--','LineWidth',2) legend('ncx2','chi2','Location','NW')
 Johnson, N., and S. Kotz. Distributions in Statistics: Continuous Univariate Distributions-2. Hoboken, NJ: John Wiley & Sons, Inc., 1970, pp. 130–148.