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<div class="title">RANDGAMMA Generate Gamma-Distributed Random Variable </div> </div>
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<div class="textblock"><p>Section: <a class="el" href="sec_random.html">Random Number Generation</a> </p>
<h1><a class="anchor" id="Usage"></a>
Usage</h1>
<p>Generates random variables with a gamma distribution. The general syntax for its use is </p>
<pre class="fragment"> 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>. </p>
<h1><a class="anchor" id="Function"></a>
Internals</h1>
<p>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>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ P(x) = \frac{a^r x^{r-1} e^{-ax}}{\Gamma(r)}. \]" src="form_144.png"/>
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<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>. </p>
<h1><a class="anchor" id="Example"></a>
Example</h1>
<p>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.</p>
<pre class="fragment">--> randgamma(1,15*ones(1,9))
ans =
Columns 1 to 7
10.0227 12.4783 18.0388 21.7056 14.1249 15.9260 22.0177
Columns 8 to 9
15.9170 24.3781
--> sum(randexp(ones(15,9)))
ans =
Columns 1 to 7
14.5031 12.8908 10.5201 16.9976 9.8463 12.7479 13.6879
Columns 8 to 9
21.7005 11.4172
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