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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<TITLE>RANDGAMMA Generate Gamma-Distributed Random Variable
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<H2>RANDGAMMA Generate Gamma-Distributed Random Variable
</H2>
<P>
Section: <A HREF=sec_random.html> Random Number Generation </A>
<H3>Usage</H3>
Generates random variables with a gamma distribution. The general
syntax for its use is
<PRE>
y = randgamma(a,r),
</PRE>
<P>
where <code>a</code> and <code>r</code> are vectors describing the parameters of the
gamma distribution. Roughly speaking, if <code>a</code> is the mean time between
changes of a Poisson random process, and we wait for the <code>r</code> change,
the resulting wait time is Gamma distributed with parameters <code>a</code>
and <code>r</code>.
<H3>Function Internals</H3>
The Gamma distribution arises in Poisson random processes. It represents
the waiting time to the occurance of the <code>r</code>-th event in a process with
mean time <code>a</code> between events. The probability distribution of a Gamma
random variable is
<P>
<DIV ALIGN="CENTER">
<IMG SRC="randgamma_eqn1.png">
</DIV>
<P>
Note also that for integer values of <code>r</code> that a Gamma random variable
is effectively the sum of <code>r</code> exponential random variables with parameter
<code>a</code>.
<H3>Example</H3>
Here we use the <code>randgamma</code> function to generate Gamma-distributed
random variables, and then generate them again using the <code>randexp</code>
function.
<PRE>
--> randgamma(1,15*ones(1,9))
ans =
Columns 1 to 8
22.7804 11.5514 16.8537 12.7457 16.2303 10.7442 19.3942 16.3611
Columns 9 to 9
17.4772
--> sum(randexp(ones(15,9)))
ans =
Columns 1 to 8
14.6404 15.1860 13.3147 11.4380 7.2307 10.8225 14.5271 12.4631
Columns 9 to 9
11.8753
</PRE>
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