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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.dist_ref.dist_algorithms"></a><a class="link" href="dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a>
  28 </h3></div></div></div>
  29 <h5>
  30 <a name="math_toolkit.dist_ref.dist_algorithms.h0"></a>
  31         <span class="phrase"><a name="math_toolkit.dist_ref.dist_algorithms.finding_the_location_and_scale_f"></a></span><a class="link" href="dist_algorithms.html#math_toolkit.dist_ref.dist_algorithms.finding_the_location_and_scale_f">Finding
  32         the Location and Scale for Normal and similar distributions</a>
  33       </h5>
  34 <p>
  35         Two functions aid finding location and scale of random variable z to give
  36         probability p (given a scale or location). Only applies to distributions
  37         like normal, lognormal, extreme value, Cauchy, (and symmetrical triangular),
  38         that have scale and location properties.
  39       </p>
  40 <p>
  41         These functions are useful to predict the mean and/or standard deviation
  42         that will be needed to meet a specified minimum weight or maximum dose.
  43       </p>
  44 <p>
  45         Complement versions are also provided, both with explicit and implicit (default)
  46         policy.
  47       </p>
  48 <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">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">;</span> <span class="comment">// May be needed by users defining their own policies.</span>
  49 <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">complement</span><span class="special">;</span> <span class="comment">// Will be needed by users who want to use complements.</span>
  50 </pre>
  51 <h5>
  52 <a name="math_toolkit.dist_ref.dist_algorithms.h1"></a>
  53         <span class="phrase"><a name="math_toolkit.dist_ref.dist_algorithms.find_location_function"></a></span><a class="link" href="dist_algorithms.html#math_toolkit.dist_ref.dist_algorithms.find_location_function">find_location
  54         function</a>
  55       </h5>
  56 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">find_location</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
  57 <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>
  58
  59 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Dist</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="comment">// explicit error handling policy</span>
  60   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">find_location</span><span class="special">(</span> <span class="comment">// For example, normal mean.</span>
  61   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">z</span><span class="special">,</span> <span class="comment">// location of random variable z to give probability, P(X &gt; z) == p.</span>
  62   <span class="comment">// For example, a nominal minimum acceptable z, so that p * 100 % are &gt; z</span>
  63   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">p</span><span class="special">,</span> <span class="comment">// probability value desired at x, say 0.95 for 95% &gt; z.</span>
  64   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">scale</span><span class="special">,</span> <span class="comment">// scale parameter, for example, normal standard deviation.</span>
  65   <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
  66
  67 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Dist</span><span class="special">&gt;</span>  <span class="comment">// with default policy.</span>
  68   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">find_location</span><span class="special">(</span> <span class="comment">// For example, normal mean.</span>
  69   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">z</span><span class="special">,</span> <span class="comment">// location of random variable z to give probability, P(X &gt; z) == p.</span>
  70   <span class="comment">// For example, a nominal minimum acceptable z, so that p * 100 % are &gt; z</span>
  71   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">p</span><span class="special">,</span> <span class="comment">// probability value desired at x, say 0.95 for 95% &gt; z.</span>
  72   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">scale</span><span class="special">);</span> <span class="comment">// scale parameter, for example, normal standard deviation.</span>
  73
  74   <span class="special">}}</span> <span class="comment">// namespaces</span>
  75 </pre>
  76 <h5>
  77 <a name="math_toolkit.dist_ref.dist_algorithms.h2"></a>
  78         <span class="phrase"><a name="math_toolkit.dist_ref.dist_algorithms.find_scale_function"></a></span><a class="link" href="dist_algorithms.html#math_toolkit.dist_ref.dist_algorithms.find_scale_function">find_scale
  79         function</a>
  80       </h5>
  81 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">find_scale</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
  82 <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>
  83
  84 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Dist</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>
  85   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">find_scale</span><span class="special">(</span> <span class="comment">// For example, normal mean.</span>
  86   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">z</span><span class="special">,</span> <span class="comment">// location of random variable z to give probability, P(X &gt; z) == p.</span>
  87   <span class="comment">// For example, a nominal minimum acceptable weight z, so that p * 100 % are &gt; z</span>
  88   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">p</span><span class="special">,</span> <span class="comment">// probability value desired at x, say 0.95 for 95% &gt; z.</span>
  89   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">location</span><span class="special">,</span> <span class="comment">// location parameter, for example, normal distribution mean.</span>
  90   <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
  91
  92  <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Dist</span><span class="special">&gt;</span> <span class="comment">// with default policy.</span>
  93    <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">find_scale</span><span class="special">(</span> <span class="comment">// For example, normal mean.</span>
  94    <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">z</span><span class="special">,</span> <span class="comment">// location of random variable z to give probability, P(X &gt; z) == p.</span>
  95    <span class="comment">// For example, a nominal minimum acceptable z, so that p * 100 % are &gt; z</span>
  96    <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">p</span><span class="special">,</span> <span class="comment">// probability value desired at x, say 0.95 for 95% &gt; z.</span>
  97    <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">location</span><span class="special">)</span> <span class="comment">// location parameter, for example, normal distribution mean.</span>
  98 <span class="special">}}</span> <span class="comment">// namespaces</span>
  99 </pre>
 100 <p>
 101         All argument must be finite, otherwise <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
 102         is called.
 103       </p>
 104 <p>
 105         Probability arguments must be [0, 1], otherwise <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
 106         is called.
 107       </p>
 108 <p>
 109         If the choice of arguments would give a negative scale, <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
 110         is called, unless the policy is to ignore, when the negative (impossible)
 111         value of scale is returned.
 112       </p>
 113 <p>
 114         <a class="link" href="../stat_tut/weg/find_eg.html" title="Find Location and Scale Examples">Find Mean and standard
 115         deviation examples</a> gives simple examples of use of both find_scale
 116         and find_location, and a longer example finding means and standard deviations
 117         of normally distributed weights to meet a specification.
 118       </p>
 119 </div>
 120 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 121 <td align="left"></td>
 122 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
 123       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
 124       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
 125       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
 126       Daryle Walker and Xiaogang Zhang<p>
 127         Distributed under the Boost Software License, Version 1.0. (See accompanying
 128         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
 129       </p>
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