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. A scalar input is expanded to a constant array with the same dimensions as the other input. The degrees of freedom parameters in v must be positive, and the values in x must lie on the interval [0 Inf].

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

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

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

Compute Chi-Square CDF

probability = chi2cdf(5,1:5)

probability = 1×5

    0.9747    0.9179    0.8282    0.7127    0.5841

probability = chi2cdf(1:5,1:5)

probability = 1×5

    0.6827    0.6321    0.6084    0.5940    0.5841

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).