<title>Geometric 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">geometric_distribution</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">geometric_distribution</span><span class="special"><></span> <span class="identifier">geometric</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">geometric_distribution</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
</p>
<p>
The probability that there are <span class="emphasis"><em>k</em></span> failures before the
- first success is
- </p>
-<p>
-    Pr(Y=<span class="emphasis"><em>k</em></span>) = (1-<span class="emphasis"><em>p</em></span>)<sup><span class="emphasis"><em>k</em></span></sup><span class="emphasis"><em>p</em></span>
+ first success
</p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">Pr(Y=<span class="emphasis"><em>k</em></span>) = (1-<span class="emphasis"><em>p</em></span>)<sup><span class="emphasis"><em>k</em></span></sup> <span class="emphasis"><em>p</em></span></span>
+ </p></blockquote></div>
<p>
For example, when throwing a 6-face dice the success probability <span class="emphasis"><em>p</em></span>
- = 1/6 = 0.1666 ̇  . Throwing repeatedly until a <span class="emphasis"><em>three</em></span>
+ = 1/6 = 0.1666 ̇. Throwing repeatedly until a <span class="emphasis"><em>three</em></span>
appears, the probability distribution of the number of times <span class="emphasis"><em>not-a-three</em></span>
is thrown is geometric.
</p>
<p>
Geometric distribution has the Probability Density Function PDF:
</p>
-<p>
-    (1-<span class="emphasis"><em>p</em></span>)<sup><span class="emphasis"><em>k</em></span></sup><span class="emphasis"><em>p</em></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">(1-<span class="emphasis"><em>p</em></span>)<sup><span class="emphasis"><em>k</em></span></sup> <span class="emphasis"><em>p</em></span></span>
+ </p></blockquote></div>
<p>
The following graph illustrates how the PDF and CDF vary for three examples
of the success fraction <span class="emphasis"><em>p</em></span>, (when considering the geometric
distribution as a continuous function),
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/geometric_pdf_2.svg" align="middle"></span>
- </p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/geometric_cdf_2.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/geometric_pdf_2.svg" align="middle"></span>
+
+ </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/geometric_cdf_2.svg" align="middle"></span>
+
+ </p></blockquote></div>
<p>
and as discrete.
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/geometric_pdf_discrete.svg" align="middle"></span>
- </p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/geometric_cdf_discrete.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/geometric_pdf_discrete.svg" align="middle"></span>
+
+ </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/geometric_cdf_discrete.svg" align="middle"></span>
+
+ </p></blockquote></div>
<h5>
<a name="math_toolkit.dist_ref.dists.geometric_dist.h0"></a>
<span class="phrase"><a name="math_toolkit.dist_ref.dists.geometric_dist.related_distributions"></a></span><a class="link" href="geometric_dist.html#math_toolkit.dist_ref.dists.geometric_dist.related_distributions">Related