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# chi2inv

Chi-square inverse cumulative distribution function

## Syntax

```X = chi2inv(P,V) ```

## Description

`X = chi2inv(P,V)` computes the inverse of the chi-square cdf with degrees of freedom specified by `V` for the corresponding probabilities in `P`. `P` and `V` can be vectors, matrices, or multidimensional arrays that have the same size. A scalar input is expanded to a constant array with the same dimensions as the other inputs. The degrees of freedom parameters in `V` must be positive, and the values in `P` must lie in the interval `[0 1]`.

The inverse chi-square cdf for a given probability p and ν degrees of freedom is

`$x={F}^{-1}\left(p|\nu \right)=\left\{x:F\left(x|\nu \right)=p\right\}$`

where

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

and Γ( · ) is the Gamma function. Each element of output `X` is the value whose cumulative probability under the chi-square cdf defined by the corresponding degrees of freedom parameter in `V` is specified by the corresponding value in `P`.

## Examples

Find a value that exceeds 95% of the samples from a chi-square distribution with 10 degrees of freedom.

```x = chi2inv(0.95,10) x = 18.3070 ```

You would observe values greater than 18.3 only 5% of the time by chance.

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