chi2inv (Statistics Toolbox)

Inverse of the chi-square (²) cumulative distribution function (cdf)

Syntax

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

Description

X = chi2inv(P,V) computes the inverse of the ² cdf with parameters specified by V for the corresponding probabilities in P. Vector or matrix inputs for P and V must have the same size. A scalar input is expanded to a constant matrix with the same dimensions as the other inputs.

The degrees of freedom parameters in V must be positive integers, and the values in P must lie in the interval [0 1].

The inverse ² cdf for a given probability p and degrees of freedom is

where

and ( · ) is the Gamma function. Each element of output X is the value whose cumulative probability under the ² 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 ² 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.

chi2cdf chi2pdf