<title>Pareto Distribution</title>
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<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
- <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a> <span class="special">=</span> <a class="link" href="../../pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
+ <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a> <span class="special">=</span> <a class="link" href="../../pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">pareto_distribution</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">pareto_distribution</span><span class="special"><></span> <span class="identifier">pareto</span><span class="special">;</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
<span class="keyword">class</span> <span class="identifier">pareto_distribution</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
distribution</a> is a continuous distribution with the <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">probability
density function (pdf)</a>:
</p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">f(x; α, β) = αβ<sup>α</sup> / x<sup>α+ 1</sup></span>
+ </p></blockquote></div>
<p>
- f(x; α, β) = αβ<sup>α</sup> / x<sup>α+ 1</sup>
- </p>
-<p>
- For shape parameter α   > 0, and scale parameter β   > 0. If x < β  , the
+ For shape parameter α > 0, and scale parameter β > 0. If x < β, the
pdf is zero.
</p>
<p>
The following graph illustrates how the PDF varies with the scale parameter
β:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/pareto_pdf1.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/pareto_pdf1.svg" align="middle"></span>
+
+ </p></blockquote></div>
<p>
And this graph illustrates how the PDF varies with the shape parameter
α:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/pareto_pdf2.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/pareto_pdf2.svg" align="middle"></span>
+
+ </p></blockquote></div>
<h5>
<a name="math_toolkit.dist_ref.dists.pareto.h0"></a>
<span class="phrase"><a name="math_toolkit.dist_ref.dists.pareto.related_distributions"></a></span><a class="link" href="pareto.html#math_toolkit.dist_ref.dists.pareto.related_distributions">Related
<span class="phrase"><a name="math_toolkit.dist_ref.dists.pareto.implementation"></a></span><a class="link" href="pareto.html#math_toolkit.dist_ref.dists.pareto.implementation">Implementation</a>
</h5>
<p>
- In the following table α   is the shape parameter of the distribution, and
- β   is its scale parameter, <span class="emphasis"><em>x</em></span> is the random variate,
+ In the following table α is the shape parameter of the distribution, and
+ β is its scale parameter, <span class="emphasis"><em>x</em></span> is the random variate,
<span class="emphasis"><em>p</em></span> is the probability and its complement <span class="emphasis"><em>q
= 1-p</em></span>.
</p>
</td>
<td>
<p>
- Using the relation: cdf p = 1 - (β   / x)<sup>α</sup>
+ Using the relation: cdf p = 1 - (β / x)<sup>α</sup>
</p>
</td>
</tr>
</td>
<td>
<p>
- Using the relation: q = 1 - p = -(β   / x)<sup>α</sup>
+ Using the relation: q = 1 - p = -(β / x)<sup>α</sup>
</p>
</td>
</tr>