Imported Upstream version 1.72.0

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

diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/arcine_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/arcine_dist.html
index 2c1151e..cbfc5b3 100644 (file)
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/arcine_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/arcine_dist.html
@@ -4,7 +4,7 @@
 <title>Arcsine 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="../dists.html" title="Distributions">
 <link rel="next" href="bernoulli_dist.html" title="Bernoulli Distribution">
@@ -30,12 +30,12 @@
 <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">arcsine_distribution</span><span class="special">;</span>
 
 <span class="keyword">typedef</span> <span class="identifier">arcsine_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">arcsine</span><span class="special">;</span> <span class="comment">// double precision standard arcsine distribution [0,1].</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">arcsine_distribution</span>
 <span class="special">{</span>
 <span class="keyword">public</span><span class="special">:</span>
@@ -82,9 +82,10 @@
           distribution</a> defined on the interval [<span class="emphasis"><em>x_min, x_max</em></span>]
           is given by:
         </p>
-<p>
-          &#8199;  &#8199; f(x; x_min, x_max) = 1 /(&#960;&#8901;&#8730;((x - x_min)&#8901;(x_max - x_min))
-        </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+            <span class="serif_italic">f(x; x_min, x_max) = 1 /(&#960;&#8901;&#8730;((x - x_min)&#8901;(x_max
+            - x_min))</span>
+          </p></blockquote></div>
 <p>
           For example, <a href="http://www.wolframalpha.com/" target="_top">Wolfram Alpha</a>
           arcsine distribution, from input of
@@ -113,18 +114,21 @@
           The 'Standard' (0, 1) arcsine distribution is shown in blue and some generalized
           examples with other <span class="emphasis"><em>x</em></span> ranges.
         </p>
-<p>
-          <span class="inlinemediaobject"><img src="../../../../graphs/arcsine_pdf.svg" align="middle"></span>
-        </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+            <span class="inlinemediaobject"><img src="../../../../graphs/arcsine_pdf.svg" align="middle"></span>
+
+          </p></blockquote></div>
 <p>
           The Cumulative Distribution Function CDF is defined as
         </p>
-<p>
-          &#8199;   &#8199;  F(x) = 2&#8901;arcsin(&#8730;((x-x_min)/(x_max - x))) / &#960;
-        </p>
-<p>
-          <span class="inlinemediaobject"><img src="../../../../graphs/arcsine_cdf.svg" align="middle"></span>
-        </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+            <span class="serif_italic">F(x) = 2&#8901;arcsin(&#8730;((x-x_min)/(x_max - x))) /
+            &#960;</span>
+          </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+            <span class="inlinemediaobject"><img src="../../../../graphs/arcsine_cdf.svg" align="middle"></span>
+
+          </p></blockquote></div>
 <h6>
 <a name="math_toolkit.dist_ref.dists.arcine_dist.h0"></a>
           <span class="phrase"><a name="math_toolkit.dist_ref.dists.arcine_dist.constructor"></a></span><a class="link" href="arcine_dist.html#math_toolkit.dist_ref.dists.arcine_dist.constructor">Constructor</a>
@@ -176,8 +180,8 @@
 <pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">arcsine_distribution</span><span class="special">;</span>
 
 <span class="identifier">arcsine_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">as</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">5</span><span class="special">);</span> <span class="comment">// Cconstructs a double arcsine distribution.</span>
-<span class="identifier">assert</span><span class="special">(</span><span class="identifier">as</span><span class="special">.</span><span class="identifier">x_min</span><span class="special">()</span> <span class="special">==</span> <span class="number">2.</span><span class="special">);</span>  <span class="comment">// as.x_min() returns 2.</span>
-<span class="identifier">assert</span><span class="special">(</span><span class="identifier">as</span><span class="special">.</span><span class="identifier">x_max</span><span class="special">()</span> <span class="special">==</span> <span class="number">5.</span><span class="special">);</span>   <span class="comment">// as.x_max()  returns 5.</span>
+<span class="identifier">BOOST_ASSERT</span><span class="special">(</span><span class="identifier">as</span><span class="special">.</span><span class="identifier">x_min</span><span class="special">()</span> <span class="special">==</span> <span class="number">2.</span><span class="special">);</span>  <span class="comment">// as.x_min() returns 2.</span>
+<span class="identifier">BOOST_ASSERT</span><span class="special">(</span><span class="identifier">as</span><span class="special">.</span><span class="identifier">x_max</span><span class="special">()</span> <span class="special">==</span> <span class="number">5.</span><span class="special">);</span>   <span class="comment">// as.x_max()  returns 5.</span>
 </pre>
 <h5>
 <a name="math_toolkit.dist_ref.dists.arcine_dist.h2"></a>
@@ -234,9 +238,9 @@
           and <span class="emphasis"><em>x_max</em></span> a fraction can be obtained from <span class="emphasis"><em>x</em></span>
           using
         </p>
-<p>
-          &#8198; fraction = (x - x_min) / (x_max - x_min)
-        </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+            <span class="serif_italic">fraction = (x - x_min) / (x_max - x_min)</span>
+          </p></blockquote></div>
 <p>
           The simplest example is tossing heads and tails with a fair coin and modelling
           the risk of losing, or winning. Walkers (molecules, drunks...) moving left
@@ -368,7 +372,7 @@
           <a href="http://www.wolframalpha.com/" target="_top">Wolfram Alpha</a>, for example:
         </p>
 <pre class="programlisting"><span class="identifier">N</span><span class="special">[</span><span class="identifier">PDF</span><span class="special">[</span><span class="identifier">arcsinedistribution</span><span class="special">[</span><span class="number">0</span><span class="special">,</span> <span class="number">1</span><span class="special">],</span> <span class="number">0.5</span><span class="special">],</span> <span class="number">50</span><span class="special">]</span>
-  <span class="number">0.63661977236758134307553505349005744813783858296183</span>
+<span class="number">0.63661977236758134307553505349005744813783858296183</span>
 </pre>
 <h5>
 <a name="math_toolkit.dist_ref.dists.arcine_dist.h7"></a>
@@ -376,7 +380,7 @@
         </h5>
 <p>
           In the following table <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>
-          are the parameters <span class="emphasis"><em>x_min</em></span> &#160; and <span class="emphasis"><em>x_max</em></span>,
+          are the parameters <span class="emphasis"><em>x_min</em></span> and <span class="emphasis"><em>x_max</em></span>,
           <span class="emphasis"><em>x</em></span> is the random variable, <span class="emphasis"><em>p</em></span> is
           the probability and its complement <span class="emphasis"><em>q = 1-p</em></span>.
         </p>
@@ -570,8 +574,9 @@
 <p>
           and produced the resulting expression
         </p>
-<pre class="programlisting"><span class="identifier">x</span> <span class="special">=</span> <span class="special">-</span><span class="identifier">a</span> <span class="identifier">sin</span><span class="special">^</span><span class="number">2</span><span class="special">((</span><span class="identifier">pi</span> <span class="identifier">p</span><span class="special">)/</span><span class="number">2</span><span class="special">)+</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span> <span class="identifier">sin</span><span class="special">^</span><span class="number">2</span><span class="special">((</span><span class="identifier">pi</span> <span class="identifier">p</span><span class="special">)/</span><span class="number">2</span><span class="special">)</span>
-</pre>
+<div class="blockquote"><blockquote class="blockquote"><p>
+            <span class="serif_italic">x = -a sin^2((pi p)/2)+a+b sin^2((pi p)/2)</span>
+          </p></blockquote></div>
 <p>
           Thanks to Wolfram for providing this facility.
         </p>