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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">&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>
<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">&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="Policies">Policy</a><span class="special">&gt;</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 &gt; z) == p.
</span> <span class="comment">// For example, a nominal minimum acceptable z, so that p * 100 % are &gt; 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% &gt; 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">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
<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> <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 &gt; z) == p.
</span> <span class="comment">// For example, a nominal minimum acceptable z, so that p * 100 % are &gt; 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% &gt; 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">&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>
<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">&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="Policies">Policy</a><span class="special">&gt;</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 &gt; z) == p.
</span> <span class="comment">// For example, a nominal minimum acceptable weight z, so that p * 100 % are &gt; 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% &gt; 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">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
<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> <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 &gt; z) == p.
</span> <span class="comment">// For example, a nominal minimum acceptable z, so that p * 100 % are &gt; 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% &gt; 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 &#169; 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan R&#229;de, 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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