<title>Inverse Chi Squared 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_chi_squared_distribution</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
= 1.
</p>
<p>
- Both definitions are also available in Wolfram Mathematica and in <a href="http://www.r-project.org/" target="_top">The R Project for Statistical Computing</a>
- (geoR) with default scale = 1/degrees of freedom.
+ Both definitions are also available in <a href="http://www.wolfram.com/products/mathematica/index.html" target="_top">Wolfram
+ Mathematica</a> and in <a href="http://www.r-project.org/" target="_top">The R
+ Project for Statistical Computing</a> (geoR) with default scale = 1/degrees
+ of freedom.
</p>
<p>
See
The inverse_chi_squared distribution is a special case of a inverse_gamma
distribution with ν (degrees_of_freedom) shape (α) and scale (β) where
</p>
-<p>
-    α= ν /2 and β = ½.
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">α= ν /2 and β = ½</span>
+ </p></blockquote></div>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td>
inverse chi_squared distribution is defined by the probability density
function (PDF):
</p>
-<p>
-    f(x;ν) = 2<sup>-ν/2</sup> x<sup>-ν/2-1</sup> e<sup>-1/2x</sup> / Γ(ν/2)
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">f(x;ν) = 2<sup>-ν/2</sup> x<sup>-ν/2-1</sup> e<sup>-1/2x</sup> / Γ(ν/2)</span>
+ </p></blockquote></div>
<p>
and Cumulative Density Function (CDF)
</p>
-<p>
-    F(x;ν) = Γ(ν/2, 1/2x) / Γ(ν/2)
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">F(x;ν) = Γ(ν/2, 1/2x) / Γ(ν/2)</span>
+ </p></blockquote></div>
<p>
For degrees of freedom parameter ν and scale parameter ξ, the <span class="bold"><strong>scaled</strong></span>
inverse chi_squared distribution is defined by the probability density
function (PDF):
</p>
-<p>
-    f(x;ν, ξ) = (ξν/2)<sup>ν/2</sup> e<sup>-νξ/2x</sup> x<sup>-1-ν/2</sup> / Γ(ν/2)
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">f(x;ν, ξ) = (ξν/2)<sup>ν/2</sup> e<sup>-νξ/2x</sup> x<sup>-1-ν/2</sup> / Γ(ν/2)</span>
+ </p></blockquote></div>
<p>
and Cumulative Density Function (CDF)
</p>
-<p>
-    F(x;ν, ξ) = Γ(ν/2, νξ/2x) / Γ(ν/2)
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">F(x;ν, ξ) = Γ(ν/2, νξ/2x) / Γ(ν/2)</span>
+ </p></blockquote></div>
<p>
The following graphs illustrate how the PDF and CDF of the inverse chi_squared
distribution varies for a few values of parameters ν and ξ:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/inverse_chi_squared_pdf.svg" align="middle"></span>
- </p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/inverse_chi_squared_cdf.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/inverse_chi_squared_pdf.svg" align="middle"></span>
+
+ </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/inverse_chi_squared_cdf.svg" align="middle"></span>
+
+ </p></blockquote></div>
<h5>
<a name="math_toolkit.dist_ref.dists.inverse_chi_squared_dist.h0"></a>
<span class="phrase"><a name="math_toolkit.dist_ref.dists.inverse_chi_squared_dist.member_functions"></a></span><a class="link" href="inverse_chi_squared_dist.html#math_toolkit.dist_ref.dists.inverse_chi_squared_dist.member_functions">Member
</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>
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