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# 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

expand 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```