<title>Negative Binomial 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">negative_binomial_distribution</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">negative_binomial_distribution</span><span class="special"><></span> <span class="identifier">negative_binomial</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">negative_binomial_distribution</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<p>
It has the PDF:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../equations/neg_binomial_ref.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../equations/neg_binomial_ref.svg"></span>
+
+ </p></blockquote></div>
<p>
The following graph illustrate how the PDF varies as the success fraction
<span class="emphasis"><em>p</em></span> changes:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/negative_binomial_pdf_1.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/negative_binomial_pdf_1.svg" align="middle"></span>
+
+ </p></blockquote></div>
<p>
Alternatively, this graph shows how the shape of the PDF varies as the
number of successes changes:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/negative_binomial_pdf_2.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/negative_binomial_pdf_2.svg" align="middle"></span>
+
+ </p></blockquote></div>
<h5>
<a name="math_toolkit.dist_ref.dists.negative_binomial_dist.h0"></a>
<span class="phrase"><a name="math_toolkit.dist_ref.dists.negative_binomial_dist.related_distributions"></a></span><a class="link" href="negative_binomial_dist.html#math_toolkit.dist_ref.dists.negative_binomial_dist.related_distributions">Related
The Poisson distribution is a special case for large successes
</p>
<p>
- poisson(λ) = lim <sub>r → ∞</sub>   negative_binomial(r, r / (λ + r)))
+ poisson(λ) = lim <sub>r → ∞</sub> negative_binomial(r, r / (λ + r)))
</p>
<div class="caution"><table border="0" summary="Caution">
<tr>