# chi2cdf

Chi-square cumulative distribution function

## Syntax

`p = chi2cdf(x,v)p = chi2cdf(x,v,'upper')`

## Description

`p = chi2cdf(x,v)` computes the chi-square cdf at each of the values in `x` using the corresponding degrees of freedom in `v`. `x` and `v` can be vectors, matrices, or multidimensional arrays that have the same size. The degrees of freedom parameters in `v` must be positive integers, and the values in `x` must lie on the interval `[0 Inf]`. A scalar input is expanded to a constant array with the same dimensions as the other input.

`p = chi2cdf(x,v,'upper')` returns the complement of the chi-square cdf at each value in `x`, using an algorithm that more accurately computes the extreme upper tail probabilities.

The χ2 cdf for a given value x and degrees-of-freedom ν is

$p=F\left(x|\nu \right)={\int }_{0}^{x}\frac{{t}^{\left(\nu -2\right)/2}{e}^{-t/2}}{{2}^{\nu /2}\Gamma \left(\nu /2\right)}dt$

where Γ( · ) is the Gamma function.

The chi-square density function with ν degrees-of-freedom is the same as the gamma density function with parameters ν/2 and 2.

## Examples

collapse all

### Compute Chi-Square CDF

`probability = chi2cdf(5,1:5)`
```probability = 0.9747 0.9179 0.8282 0.7127 0.5841```
`probability = chi2cdf(1:5,1:5)`
```probability = 0.6827 0.6321 0.6084 0.5940 0.5841```