<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Distribution Algorithms</title> <link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.74.0"> <link rel="home" href="../../../index.html" title="Math Toolkit"> <link rel="up" href="../dist_ref.html" title="Statistical Distributions Reference"> <link rel="prev" href="dists/uniform_dist.html" title="Uniform Distribution"> <link rel="next" href="../future.html" title="Extras/Future Directions"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> <table cellpadding="2" width="100%"><tr> <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../../boost.png"></td> <td align="center"><a href="../../../../../../../../index.html">Home</a></td> <td align="center"><a href="../../../../../../../../libs/libraries.htm">Libraries</a></td> <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> <td align="center"><a href="../../../../../../../../more/index.htm">More</a></td> </tr></table> <hr> <div class="spirit-nav"> <a accesskey="p" href="dists/uniform_dist.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../future.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> <div class="section" lang="en"> <div class="titlepage"><div><div><h4 class="title"> <a name="math_toolkit.dist.dist_ref.dist_algorithms"></a><a class="link" href="dist_algorithms.html" title="Distribution Algorithms"> Distribution Algorithms</a> </h4></div></div></div> <a name="math_toolkit.dist.dist_ref.dist_algorithms.finding_the_location_and_scale_for_normal_and_similar_distributions"></a><h5> <a name="id1068406"></a> <a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.finding_the_location_and_scale_for_normal_and_similar_distributions">Finding the Location and Scale for Normal and similar distributions</a> </h5> <p> Two functions aid finding location and scale of random variable z to give probability p (given a scale or location). Only applies to distributions like normal, lognormal, extreme value, Cauchy, (and symmetrical triangular), that have scale and location properties. </p> <p> These functions are useful to predict the mean and/or standard deviation that will be needed to meet a specified minimum weight or maximum dose. </p> <p> Complement versions are also provided, both with explicit and implicit (default) policy. </p> <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><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></pre> <a name="math_toolkit.dist.dist_ref.dist_algorithms.find_location_function"></a><h5> <a name="id1068504"></a> <a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.find_location_function">find_location function</a> </h5> <p> </p> <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</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">></span></pre> <p> </p> <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">Dist</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span> <span class="comment">// explicit error handling policy </span> <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> <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 > z) == p. </span> <span class="comment">// For example, a nominal minimum acceptable z, so that p * 100 % are > z </span> <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% > z. </span> <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> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&</span> <span class="identifier">pol</span><span class="special">);</span> <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Dist</span><span class="special">></span> <span class="comment">// with default policy. </span> <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> <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 > z) == p. </span> <span class="comment">// For example, a nominal minimum acceptable z, so that p * 100 % are > z </span> <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% > z. </span> <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> <span class="special">}}</span> <span class="comment">// namespaces </span></pre> <a name="math_toolkit.dist.dist_ref.dist_algorithms.find_scale_function"></a><h5> <a name="id1068949"></a> <a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.find_scale_function">find_scale function</a> </h5> <p> </p> <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</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">></span></pre> <p> </p> <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">Dist</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span> <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> <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 > z) == p. </span> <span class="comment">// For example, a nominal minimum acceptable weight z, so that p * 100 % are > z </span> <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% > z. </span> <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> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&</span> <span class="identifier">pol</span><span class="special">);</span> <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Dist</span><span class="special">></span> <span class="comment">// with default policy. </span> <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> <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 > z) == p. </span> <span class="comment">// For example, a nominal minimum acceptable z, so that p * 100 % are > z </span> <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% > z. </span> <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><span class="special">}}</span> <span class="comment">// namespaces </span></pre> <p> All argument must be finite, otherwise <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a> is called. </p> <p> Probability arguments must be [0, 1], otherwise <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a> is called. </p> <p> If the choice of arguments would give a negative scale, <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a> is called, unless the policy is to ignore, when the negative (impossible) value of scale is returned. </p> <p> <a class="link" href="../stat_tut/weg/find_eg.html" title="Find Location and Scale Examples">Find Mean and standard deviation examples</a> gives simple examples of use of both find_scale and find_location, and a longer example finding means and standard deviations of normally distributed weights to meet a specification. </p> </div> <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> Distributed under the Boost Software License, Version 1.0. (See accompanying 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>) </p> </div></td> </tr></table> <hr> <div class="spirit-nav"> <a accesskey="p" href="dists/uniform_dist.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../future.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html>