<title>Hyperexponential Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.11.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="geometric_dist.html" title="Geometric Distribution">
<link rel="next" href="hypergeometric_dist.html" title="Hypergeometric Distribution">
<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">typename</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
- <span class="keyword">typename</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">typename</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">hyperexponential_distribution</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">hyperexponential_distribution</span><span class="special"><></span> <span class="identifier">hyperexponential</span><span class="special">;</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">typename</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">typename</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">typename</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">hyperexponential_distribution</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
density function</a> for random variate <span class="emphasis"><em>x</em></span> in a
hyperexponential distribution is given by:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_pdf.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_pdf.svg"></span>
+
+ </p></blockquote></div>
<p>
The following graph illustrates the PDF of the hyperexponential distribution
with five different parameters, namely:
and <span class="emphasis"><em><span class="bold"><strong>λ</strong></span>=(0.5, 1.0, 1.5)</em></span>.
</li>
</ol></div>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/hyperexponential_pdf.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/hyperexponential_pdf.svg" align="middle"></span>
+
+ </p></blockquote></div>
<p>
Also, the following graph illustrates the PDF of the hyperexponential distribution
(solid lines) where only the <span class="emphasis"><em>phase probability vector</em></span>
approaches to <span class="emphasis"><em>0</em></span>), the resulting hyperexponential distribution
nears the exponential distribution with parameter <span class="emphasis"><em>λ=1.5</em></span>.
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/hyperexponential_pdf_samerate.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/hyperexponential_pdf_samerate.svg" align="middle"></span>
+
+ </p></blockquote></div>
<p>
Finally, the following graph compares the PDF of the hyperexponential distribution
with different number of phases but with the same mean value equal to
and <span class="emphasis"><em><span class="bold"><strong>λ</strong></span>=(0.2, 1.5, 3.0)</em></span>,
</li>
</ol></div>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/hyperexponential_pdf_samemean.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/hyperexponential_pdf_samemean.svg" align="middle"></span>
+
+ </p></blockquote></div>
<p>
As can be noted, even if the three distributions have the same mean value,
the two hyperexponential distributions have a <span class="emphasis"><em>longer</em></span>
<span class="identifier">hyperexponential</span> <span class="identifier">he</span><span class="special">(</span><span class="identifier">rates</span><span class="special">.</span><span class="identifier">begin</span><span class="special">(),</span> <span class="identifier">rates</span><span class="special">.</span><span class="identifier">end</span><span class="special">());</span>
-<span class="identifier">assert</span><span class="special">(</span><span class="identifier">he</span><span class="special">.</span><span class="identifier">probabilities</span><span class="special">()[</span><span class="number">0</span><span class="special">]</span> <span class="special">==</span> <span class="number">0.5</span><span class="special">);</span> <span class="comment">// Phase probabilities will be equal and normalised to unity.</span>
+<span class="identifier">BOOST_ASSERT</span><span class="special">(</span><span class="identifier">he</span><span class="special">.</span><span class="identifier">probabilities</span><span class="special">()[</span><span class="number">0</span><span class="special">]</span> <span class="special">==</span> <span class="number">0.5</span><span class="special">);</span> <span class="comment">// Phase probabilities will be equal and normalised to unity.</span>
</pre>
<h5>
<a name="math_toolkit.dist_ref.dists.hyperexponential_dist.h19"></a>
<span class="identifier">hyperexponential</span> <span class="identifier">he</span><span class="special">(</span><span class="identifier">rates</span><span class="special">);</span>
-<span class="identifier">assert</span><span class="special">(</span><span class="identifier">he</span><span class="special">.</span><span class="identifier">probabilities</span><span class="special">()[</span><span class="number">0</span><span class="special">]</span> <span class="special">==</span> <span class="number">0.5</span><span class="special">);</span> <span class="comment">// Phase probabilities will be equal and normalised to unity.</span>
+<span class="identifier">BOOST_ASSERT</span><span class="special">(</span><span class="identifier">he</span><span class="special">.</span><span class="identifier">probabilities</span><span class="special">()[</span><span class="number">0</span><span class="special">]</span> <span class="special">==</span> <span class="number">0.5</span><span class="special">);</span> <span class="comment">// Phase probabilities will be equal and normalised to unity.</span>
</pre>
<h5>
<a name="math_toolkit.dist_ref.dists.hyperexponential_dist.h23"></a>
</h6>
<pre class="programlisting"><span class="identifier">hyperexponential</span> <span class="identifier">he</span> <span class="special">=</span> <span class="special">{</span> <span class="number">1.0</span> <span class="special">/</span> <span class="number">10</span><span class="special">,</span> <span class="number">1.0</span> <span class="special">/</span> <span class="number">12</span> <span class="special">};</span>
-<span class="identifier">assert</span><span class="special">(</span><span class="identifier">he</span><span class="special">.</span><span class="identifier">probabilities</span><span class="special">()[</span><span class="number">0</span><span class="special">]</span> <span class="special">==</span> <span class="number">0.5</span><span class="special">);</span>
+<span class="identifier">BOOST_ASSERT</span><span class="special">(</span><span class="identifier">he</span><span class="special">.</span><span class="identifier">probabilities</span><span class="special">()[</span><span class="number">0</span><span class="special">]</span> <span class="special">==</span> <span class="number">0.5</span><span class="special">);</span>
</pre>
<h5>
<a name="math_toolkit.dist_ref.dists.hyperexponential_dist.h29"></a>
</p>
</td>
<td>
- <p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_pdf.svg"></span>
- </p>
+ <div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_pdf.svg"></span>
+
+ </p></blockquote></div>
</td>
</tr>
<tr>
</p>
</td>
<td>
- <p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_cdf.svg"></span>
- </p>
+ <div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_cdf.svg"></span>
+
+ </p></blockquote></div>
</td>
</tr>
<tr>
</p>
</td>
<td>
- <p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_ccdf.svg"></span>
- </p>
+ <div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_ccdf.svg"></span>
+
+ </p></blockquote></div>
</td>
</tr>
<tr>
</p>
</td>
<td>
- <p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_mean.svg"></span>
- </p>
+ <div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_mean.svg"></span>
+
+ </p></blockquote></div>
</td>
</tr>
<tr>
</p>
</td>
<td>
- <p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_variance.svg"></span>
- </p>
+ <div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_variance.svg"></span>
+
+ </p></blockquote></div>
</td>
</tr>
<tr>
</p>
</td>
<td>
- <p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_skewness.svg"></span>
- </p>
+ <div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_skewness.svg"></span>
+
+ </p></blockquote></div>
</td>
</tr>
<tr>
</p>
</td>
<td>
- <p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_kurtosis.svg"></span>
- </p>
+ <div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_kurtosis.svg"></span>
+
+ </p></blockquote></div>
</td>
</tr>
<tr>