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  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="math_toolkit.future"></a><a class="link" href="future.html" title="Extras/Future Directions">Extras/Future Directions</a>
  28 </h2></div></div></div>
  29 <h5>
  30 <a name="math_toolkit.future.h0"></a>
  31       <span class="phrase"><a name="math_toolkit.future.adding_additional_location_and_s"></a></span><a class="link" href="future.html#math_toolkit.future.adding_additional_location_and_s">Adding
  32       Additional Location and Scale Parameters</a>
  33     </h5>
  34 <p>
  35       In some modelling applications we require a distribution with a specific location
  36       and scale: often this equates to a specific mean and standard deviation, although
  37       for many distributions the relationship between these properties and the location
  38       and scale parameters are non-trivial. See <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm" target="_top">http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm</a>
  39       for more information.
  40     </p>
  41 <p>
  42       The obvious way to handle this is via an adapter template:
  43     </p>
  44 <pre class="programlisting"><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>
  45 <span class="keyword">class</span> <span class="identifier">scaled_distribution</span>
  46 <span class="special">{</span>
  47    <span class="identifier">scaled_distribution</span><span class="special">(</span>
  48      <span class="keyword">const</span> <span class="identifier">Dist</span> <span class="identifier">dist</span><span class="special">,</span>
  49      <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>
  50      <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="number">0</span><span class="special">);</span>
  51 <span class="special">};</span>
  52 </pre>
  53 <p>
  54       Which would then have its own set of overloads for the non-member accessor
  55       functions.
  56     </p>
  57 <h5>
  58 <a name="math_toolkit.future.h1"></a>
  59       <span class="phrase"><a name="math_toolkit.future.an_any_distribution_class"></a></span><a class="link" href="future.html#math_toolkit.future.an_any_distribution_class">An
  60       "any_distribution" class</a>
  61     </h5>
  62 <p>
  63       It is easy to add a distribution object that virtualises the actual type of
  64       the distribution, and can therefore hold "any" object that conforms
  65       to the conceptual requirements of a distribution:
  66     </p>
  67 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
  68 <span class="keyword">class</span> <span class="identifier">any_distribution</span>
  69 <span class="special">{</span>
  70 <span class="keyword">public</span><span class="special">:</span>
  71    <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Distribution</span><span class="special">&gt;</span>
  72    <span class="identifier">any_distribution</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Distribution</span><span class="special">&amp;</span> <span class="identifier">d</span><span class="special">);</span>
  73 <span class="special">};</span>
  74
  75 <span class="comment">// Get the cdf of the underlying distribution:</span>
  76 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
  77 <span class="identifier">RealType</span> <span class="identifier">cdf</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">any_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;&amp;</span> <span class="identifier">d</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">);</span>
  78 <span class="comment">// etc....</span>
  79 </pre>
  80 <p>
  81       Such a class would facilitate the writing of non-template code that can function
  82       with any distribution type.
  83     </p>
  84 <p>
  85       The <a href="http://sourceforge.net/projects/distexplorer/" target="_top">Statistical
  86       Distribution Explorer</a> utility for Windows is a usage example.
  87     </p>
  88 <p>
  89       It's not clear yet whether there is a compelling use case though. Possibly
  90       tests for goodness of fit might provide such a use case: this needs more investigation.
  91     </p>
  92 <h5>
  93 <a name="math_toolkit.future.h2"></a>
  94       <span class="phrase"><a name="math_toolkit.future.higher_level_hypothesis_tests"></a></span><a class="link" href="future.html#math_toolkit.future.higher_level_hypothesis_tests">Higher
  95       Level Hypothesis Tests</a>
  96     </h5>
  97 <p>
  98       Higher-level tests roughly corresponding to the <a href="http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/Statistics/HypothesisTests.html" target="_top">Mathematica
  99       Hypothesis Tests</a> package could be added reasonably easily, for example:
 100     </p>
 101 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">InputIterator</span><span class="special">&gt;</span>
 102 <span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special">&lt;</span><span class="identifier">InputIterator</span><span class="special">&gt;::</span><span class="identifier">value_type</span>
 103    <span class="identifier">test_equal_mean</span><span class="special">(</span>
 104      <span class="identifier">InputIterator</span> <span class="identifier">a</span><span class="special">,</span>
 105      <span class="identifier">InputIterator</span> <span class="identifier">b</span><span class="special">,</span>
 106      <span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special">&lt;</span><span class="identifier">InputIterator</span><span class="special">&gt;::</span><span class="identifier">value_type</span> <span class="identifier">expected_mean</span><span class="special">);</span>
 107 </pre>
 108 <p>
 109       Returns the probability that the data in the sequence [a,b) has the mean <span class="emphasis"><em>expected_mean</em></span>.
 110     </p>
 111 <h5>
 112 <a name="math_toolkit.future.h3"></a>
 113       <span class="phrase"><a name="math_toolkit.future.integration_with_statistical_acc"></a></span><a class="link" href="future.html#math_toolkit.future.integration_with_statistical_acc">Integration
 114       With Statistical Accumulators</a>
 115     </h5>
 116 <p>
 117       <a href="http://boost-sandbox.sourceforge.net/libs/accumulators/doc/html/index.html" target="_top">Eric
 118       Niebler's accumulator framework</a> - also work in progress - provides
 119       the means to calculate various statistical properties from experimental data.
 120       There is an opportunity to integrate the statistical tests with this framework
 121       at some later date:
 122     </p>
 123 <pre class="programlisting"><span class="comment">// Define an accumulator, all required statistics to calculate the test</span>
 124 <span class="comment">// are calculated automatically:</span>
 125 <span class="identifier">accumulator_set</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">features</span><span class="special">&lt;</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">test_expected_mean</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">acc</span><span class="special">(</span><span class="identifier">expected_mean</span><span class="special">=</span><span class="number">4</span><span class="special">);</span>
 126 <span class="comment">// Pass our data to the accumulator:</span>
 127 <span class="identifier">acc</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">for_each</span><span class="special">(</span><span class="identifier">mydata</span><span class="special">.</span><span class="identifier">begin</span><span class="special">(),</span> <span class="identifier">mydata</span><span class="special">.</span><span class="identifier">end</span><span class="special">(),</span> <span class="identifier">acc</span><span class="special">);</span>
 128 <span class="comment">// Extract the result:</span>
 129 <span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">probability</span><span class="special">(</span><span class="identifier">acc</span><span class="special">);</span>
 130 </pre>
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 134 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 135       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 136       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
 137       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 138         Distributed under the Boost Software License, Version 1.0. (See accompanying
 139         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>)
 140       </p>
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