<title>Poisson 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">poisson_distribution</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">poisson_distribution</span><span class="special"><></span> <span class="identifier">poisson</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">poisson_distribution</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
distribution</a> is a well-known statistical discrete distribution.
It expresses the probability of a number of events (or failures, arrivals,
occurrences ...) occurring in a fixed period of time, provided these events
- occur with a known mean rate λ  
+ occur with a known mean rate λ
(events/time), and are independent of the
time since the last event.
</p>
<p>
- The distribution was discovered by Simé on-Denis Poisson (1781 to 1840).
+ The distribution was discovered by Siméon-Denis Poisson (1781 to 1840).
</p>
<p>
It has the Probability Mass Function:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../equations/poisson_ref1.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../equations/poisson_ref1.svg"></span>
+
+ </p></blockquote></div>
<p>
for k events, with an expected number of events λ.
</p>
<p>
The following graph illustrates how the PDF varies with the parameter λ:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/poisson_pdf_1.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/poisson_pdf_1.svg" align="middle"></span>
+
+ </p></blockquote></div>
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../doc/src/images/caution.png"></td>
<span class="phrase"><a name="math_toolkit.dist_ref.dists.poisson_dist.implementation"></a></span><a class="link" href="poisson_dist.html#math_toolkit.dist_ref.dists.poisson_dist.implementation">Implementation</a>
</h5>
<p>
- In the following table λ   is the mean of the distribution, <span class="emphasis"><em>k</em></span>
+ In the following table λ is the mean of the distribution, <span class="emphasis"><em>k</em></span>
is the random variable, <span class="emphasis"><em>p</em></span> is the probability and
<span class="emphasis"><em>q = 1-p</em></span>.
</p>