## RANDCHI Generate Chi-Square Random Variable

Section: Random Number Generation

### Usage

Generates a vector of chi-square random variables with the given number of degrees of freedom. The general syntax for its use isy = randchi(n)

where `n`

is an array containing the degrees of freedom for
each generated random variable.

### Function Internals

A chi-square random variable is essentially distributed as the squared Euclidean norm of a vector of standard Gaussian random variables. The number of degrees of freedom is generally the number of elements in the vector. In general, the PDF of a chi-square random variable is

### Example

First, a plot of the PDF for a family of chi-square random variables--> f = zeros(7,100); --> x = (1:100)/10; --> for n=1:7;t=x.^(n/2-1).*exp(-x/2);f(n,:)=10*t/sum(t);end --> plot(x,f');

The PDF is below:

Here is an example of using `randchi`

and `randn`

to compute
some chi-square random variables with four degrees of freedom.

--> randchi(4*ones(1,6)) ans = 8.9675 4.0015 3.2578 5.5461 2.5090 5.7587 --> sum(randn(4,6).^2) ans = 1.1941 10.6441 3.6228 8.4425 2.5031 1.9058