FreeMat: RANDCHI Generate Chi-Square Random Variable

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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 is

       y = randchi(n)

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

# 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 =
        2.6122    6.2362    0.8717    1.4935    6.0370    5.2771

    --> sum(randn(4,6).^2)

    ans =
        0.0399    4.6296    0.8697    0.5796    1.5490    5.8538