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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<TITLE>RANDF Generate F-Distributed Random Variable
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<H2>RANDF Generate F-Distributed Random Variable
</H2>
<P>
Section: <A HREF=sec_random.html> Random Number Generation </A>
<H3>Usage</H3>
Generates random variables with an F-distribution. The general
syntax for its use is
<PRE>
y = randf(n,m)
</PRE>
<P>
where <code>n</code> and <code>m</code> are vectors of the number of degrees of freedom
in the numerator and denominator of the chi-square random variables
whose ratio defines the statistic.
<H3>Function Internals</H3>
The statistic <code>F_{n,m}</code> is defined as the ratio of two chi-square
random variables:
<P>
<DIV ALIGN="CENTER">
<IMG SRC="randf_eqn1.png">
</DIV>
<P>
The PDF is given by
<P>
<DIV ALIGN="CENTER">
<IMG SRC="randf_eqn2.png">
</DIV>
<P>
where <code>B(a,b)</code> is the beta function.
<H3>Example</H3>
Here we use <code>randf</code> to generate some F-distributed random variables,
and then again using the <code>randchi</code> function:
<PRE>
--> randf(5*ones(1,9),7)
ans =
Columns 1 to 8
1.1944 0.9069 0.7558 1.5029 0.0621 1.3860 1.8161 0.3755
Columns 9 to 9
3.5794
--> randchi(5*ones(1,9))./randchi(7*ones(1,9))
ans =
Columns 1 to 8
1.3085 1.2693 1.0684 0.4377 1.1158 0.7171 0.4151 1.8022
Columns 9 to 9
1.4606
</PRE>
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