# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

# ncx2cdf

Noncentral chi-square cumulative distribution function

## Syntax

```p = ncx2cdf(x,v,delta) p = ncx2cdf(x,v,delta,'upper') ```

## Description

`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

`$F\left(x|\nu ,\delta \right)=\sum _{j=0}^{\infty }\left(\frac{{\left(\frac{1}{2}\delta \right)}^{j}}{j!}{e}^{\frac{-\delta }{2}}\right)\mathrm{Pr}\left[{\chi }_{\nu +2j}^{2}\le x\right]$`

## Examples

collapse all

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') ```

## References

[1] Johnson, N., and S. Kotz. Distributions in Statistics: Continuous Univariate Distributions-2. Hoboken, NJ: John Wiley & Sons, Inc., 1970, pp. 130–148.