<title>Inverse Gamma 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">inverse_gamma_distribution</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
For shape parameter α and scale parameter β, it is defined by the probability
density function (PDF):
</p>
-<p>
-    f(x;α, β) = β<sup>α</sup> * (1/x) <sup>α+1</sup> exp(-β/x) / Γ(α)
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">f(x;α, β) = β<sup>α</sup> * (1/x) <sup>α+1</sup> exp(-β/x) / Γ(α)</span>
+ </p></blockquote></div>
<p>
and cumulative density function (CDF)
</p>
-<p>
-    F(x;α, β) = Γ(α, β/x) / Γ(α)
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">F(x;α, β) = Γ(α, β/x) / Γ(α)</span>
+ </p></blockquote></div>
<p>
The following graphs illustrate how the PDF and CDF of the inverse gamma
distribution varies as the parameters vary:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/inverse_gamma_pdf.svg" align="middle"></span>
- </p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/inverse_gamma_cdf.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/inverse_gamma_pdf.svg" align="middle"></span>
+
+ </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/inverse_gamma_cdf.svg" align="middle"></span>
+
+ </p></blockquote></div>
<h5>
<a name="math_toolkit.dist_ref.dists.inverse_gamma_dist.h0"></a>
<span class="phrase"><a name="math_toolkit.dist_ref.dists.inverse_gamma_dist.member_functions"></a></span><a class="link" href="inverse_gamma_dist.html#math_toolkit.dist_ref.dists.inverse_gamma_dist.member_functions">Member
<span class="phrase"><a name="math_toolkit.dist_ref.dists.inverse_gamma_dist.implementation"></a></span><a class="link" href="inverse_gamma_dist.html#math_toolkit.dist_ref.dists.inverse_gamma_dist.implementation">Implementation</a>
</h5>
<p>
- In the following table α is the shape parameter of the distribution, α   is its
+ In the following table α is the shape parameter of the distribution, α 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 <span class="emphasis"><em>q = 1-p</em></span>.
</p>
</td>
<td>
<p>
- Using the relation: x = β  / <a class="link" href="../../sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>(α,
+ Using the relation: x = β/ <a class="link" href="../../sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>(α,
p)
</p>
</td>
</td>
<td>
<p>
- Using the relation: x = α  / <a class="link" href="../../sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>(α,
+ Using the relation: x = α/ <a class="link" href="../../sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>(α,
q)
</p>
</td>