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| <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="id1064551"></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="id1064649"></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="id1065232"></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> |
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| <td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009, 2010 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>) |
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