Imported Upstream version 1.72.0

[platform/upstream/boost.git] / libs / math / doc / html / math_toolkit / dist_ref / dists / nc_t_dist.html

diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_t_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_t_dist.html
index 18f31d0..3041d25 100644 (file)
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_t_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_t_dist.html
@@ -4,7 +4,7 @@
 <title>Noncentral T Distribution</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.11.0">
 <link rel="up" href="../dists.html" title="Distributions">
 <link rel="prev" href="nc_f_dist.html" title="Noncentral F Distribution">
 <link rel="next" href="normal_dist.html" title="Normal (Gaussian) Distribution">
@@ -31,12 +31,12 @@
 <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">&lt;</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&#160;19.&#160;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&lt;&gt;</a> <span class="special">&gt;</span>
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Chapter&#160;20.&#160;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&lt;&gt;</a> <span class="special">&gt;</span>
 <span class="keyword">class</span> <span class="identifier">non_central_t_distribution</span><span class="special">;</span>
 
 <span class="keyword">typedef</span> <span class="identifier">non_central_t_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">non_central_t</span><span class="special">;</span>
 
-<span class="keyword">template</span> <span class="special">&lt;</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&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<span class="keyword">template</span> <span class="special">&lt;</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&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
 <span class="keyword">class</span> <span class="identifier">non_central_t_distribution</span>
 <span class="special">{</span>
 <span class="keyword">public</span><span class="special">:</span>
@@ -58,28 +58,34 @@
 <p>
           The noncentral T distribution is a generalization of the <a class="link" href="students_t_dist.html" title="Students t Distribution">Students
           t Distribution</a>. Let X have a normal distribution with mean &#948; and variance
-          1, and let &#957; S<sup>2</sup> have a chi-squared distribution with degrees of freedom &#957;.
-          Assume that X and S<sup>2</sup> are independent. The distribution of t<sub>&#957;</sub>(&#948;)=X/S is called
-          a noncentral t distribution with degrees of freedom &#957; and noncentrality parameter
-          &#948;.
+          1, and let <span class="emphasis"><em>&#957; S<sup>2</sup></em></span> have a chi-squared distribution with
+          degrees of freedom &#957;. Assume that X and S<sup>2</sup> are independent. The distribution
+          of <span class="serif_italic">t<sub>&#957;</sub>(&#948;)=X/S</span> is called a noncentral
+          t distribution with degrees of freedom &#957; and noncentrality parameter &#948;.
         </p>
 <p>
           This gives the following PDF:
         </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+            <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref1.svg"></span>
+
+          </p></blockquote></div>
 <p>
-          <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref1.svg"></span>
-        </p>
-<p>
-          where <sub>1</sub>F<sub>1</sub>(a;b;x) is a confluent hypergeometric function.
+          where <span class="serif_italic"><sub>1</sub>F<sub>1</sub>(a;b;x)</span> is a confluent hypergeometric
+          function.
         </p>
 <p>
           The following graph illustrates how the distribution changes for different
           values of &#957; and &#948;:
         </p>
-<p>
-          <span class="inlinemediaobject"><img src="../../../../graphs/nc_t_pdf.svg" align="middle"></span>
-  <span class="inlinemediaobject"><img src="../../../../graphs/nc_t_cdf.svg" align="middle"></span>
-        </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+            <span class="inlinemediaobject"><img src="../../../../graphs/nc_t_pdf.svg" align="middle"></span>
+
+          </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+            <span class="inlinemediaobject"><img src="../../../../graphs/nc_t_cdf.svg" align="middle"></span>
+
+          </p></blockquote></div>
 <h5>
 <a name="math_toolkit.dist_ref.dists.nc_t_dist.h0"></a>
           <span class="phrase"><a name="math_toolkit.dist_ref.dists.nc_t_dist.member_functions"></a></span><a class="link" href="nc_t_dist.html#math_toolkit.dist_ref.dists.nc_t_dist.member_functions">Member
@@ -450,9 +456,10 @@ when the normal distribution
 <p>
           This uses the following formula for the CDF:
         </p>
-<p>
-          <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref2.svg"></span>
-        </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+            <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref2.svg"></span>
+
+          </p></blockquote></div>
 <p>
           Where I<sub>x</sub>(a,b) is the incomplete beta function, and &#934;(x) is the normal CDF
           at x.
@@ -466,15 +473,17 @@ when the normal distribution
           Alternatively, by considering what happens when t = &#8734;, we have x = 1, and
           therefore I<sub>x</sub>(a,b) = 1 and:
         </p>
-<p>
-          <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref3.svg"></span>
-        </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+            <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref3.svg"></span>
+
+          </p></blockquote></div>
 <p>
           From this we can easily show that:
         </p>
-<p>
-          <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref4.svg"></span>
-        </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+            <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref4.svg"></span>
+
+          </p></blockquote></div>
 <p>
           and therefore we have a means to compute either the probability or its
           complement directly without the risk of cancellation error. The crossover
@@ -485,9 +494,10 @@ when the normal distribution
 <p>
           The PDF can be computed by a very similar method using:
         </p>
-<p>
-          <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref5.svg"></span>
-        </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+            <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref5.svg"></span>
+
+          </p></blockquote></div>
 <p>
           Where I<sub>x</sub><sup>'</sup>(a,b) is the derivative of the incomplete beta function.
         </p>