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

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

where

$$p=F(x|\nu )={\displaystyle {\int }_0^x\frac{t^{(\nu -2)/2}{e}^{-t/2}}{2^{\nu /2}\Gamma (\nu /2)}}dt$$

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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).