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<div class="title">RANDBETA Beta Deviate Random Number Generator </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>Creates an array of beta random deviates based on the supplied two parameters. The general syntax for <code>randbeta</code> is </p>
<pre class="fragment"> y = randbeta(alpha, beta)
</pre><p> where <code>alpha</code> and <code>beta</code> are the two parameters of the random deviate. There are three forms for calling <code>randbeta</code>. The first uses two vectors <code>alpha</code> and <code>beta</code> of the same size, in which case the output <code>y</code> is the same size as both inputs, and each deviate uses the corresponding values of <code>alpha</code> and <code>beta</code> from the arguments. In the other forms, either <code>alpha</code> or <code>beta</code> are scalars. </p>
<h1><a class="anchor" id="Function"></a>
Internals</h1>
<p>The probability density function (PDF) of a beta random variable is </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ f(x) = x^(a-1) * (1-x)^(b-1) / B(a,b) \]" src="form_138.png"/>
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<p> for <code>x</code> between 0 and 1. The function <code>B(a,b)</code> is defined so that the integral of <code>f(x)</code> is 1. </p>
<h1><a class="anchor" id="Example"></a>
Example</h1>
<p>Here is a plot of the PDF of a beta random variable with <code>a=3</code>, <code>b=7</code>.</p>
<pre class="fragment">--> a = 3; b = 7;
--> x = (0:100)/100; t = x.^(a-1).*(1-x).^(b-1);
--> t = t/(sum(t)*.01);
--> plot(x,t);
</pre><p>which is plotted as </p>
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<img src="betapdf.png" alt="betapdf.png"/>
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If we generate a few random deviates with these values, we see they are distributed around the peak of roughly <code>0.25</code>.</p>
<pre class="fragment">--> randbeta(3*ones(1,5),7*ones(1,5))
ans =
0.4343 0.4220 0.3992 0.2727 0.2475
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