FreeMat
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Section: Random Number Generation
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.
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
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:
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