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| <div class="section"> |
| <div class="titlepage"><div><div><h2 class="title" style="clear: both"> |
| <a name="math_toolkit.future"></a><a class="link" href="future.html" title="Extras/Future Directions">Extras/Future Directions</a> |
| </h2></div></div></div> |
| <h5> |
| <a name="math_toolkit.future.h0"></a> |
| <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 |
| Additional Location and Scale Parameters</a> |
| </h5> |
| <p> |
| In some modelling applications we require a distribution with a specific location |
| and scale: often this equates to a specific mean and standard deviation, although |
| for many distributions the relationship between these properties and the location |
| 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> |
| for more information. |
| </p> |
| <p> |
| The obvious way to handle this is via an adapter template: |
| </p> |
| <pre class="programlisting"><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> <span class="identifier">scaled_distribution</span> |
| <span class="special">{</span> |
| <span class="identifier">scaled_distribution</span><span class="special">(</span> |
| <span class="keyword">const</span> <span class="identifier">Dist</span> <span class="identifier">dist</span><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">location</span><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">scale</span> <span class="special">=</span> <span class="number">0</span><span class="special">);</span> |
| <span class="special">};</span> |
| </pre> |
| <p> |
| Which would then have its own set of overloads for the non-member accessor |
| functions. |
| </p> |
| <h5> |
| <a name="math_toolkit.future.h1"></a> |
| <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 |
| "any_distribution" class</a> |
| </h5> |
| <p> |
| It is easy to add a distribution object that virtualises the actual type of |
| the distribution, and can therefore hold "any" object that conforms |
| to the conceptual requirements of a distribution: |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">></span> |
| <span class="keyword">class</span> <span class="identifier">any_distribution</span> |
| <span class="special">{</span> |
| <span class="keyword">public</span><span class="special">:</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Distribution</span><span class="special">></span> |
| <span class="identifier">any_distribution</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Distribution</span><span class="special">&</span> <span class="identifier">d</span><span class="special">);</span> |
| <span class="special">};</span> |
| |
| <span class="comment">// Get the cdf of the underlying distribution:</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">></span> |
| <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"><</span><span class="identifier">RealType</span><span class="special">>&</span> <span class="identifier">d</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">);</span> |
| <span class="comment">// etc....</span> |
| </pre> |
| <p> |
| Such a class would facilitate the writing of non-template code that can function |
| with any distribution type. |
| </p> |
| <p> |
| The <a href="http://sourceforge.net/projects/distexplorer/" target="_top">Statistical |
| Distribution Explorer</a> utility for Windows is a usage example. |
| </p> |
| <p> |
| It's not clear yet whether there is a compelling use case though. Possibly |
| tests for goodness of fit might provide such a use case: this needs more investigation. |
| </p> |
| <h5> |
| <a name="math_toolkit.future.h2"></a> |
| <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 |
| Level Hypothesis Tests</a> |
| </h5> |
| <p> |
| Higher-level tests roughly corresponding to the <a href="http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/Statistics/HypothesisTests.html" target="_top">Mathematica |
| Hypothesis Tests</a> package could be added reasonably easily, for example: |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">InputIterator</span><span class="special">></span> |
| <span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special"><</span><span class="identifier">InputIterator</span><span class="special">>::</span><span class="identifier">value_type</span> |
| <span class="identifier">test_equal_mean</span><span class="special">(</span> |
| <span class="identifier">InputIterator</span> <span class="identifier">a</span><span class="special">,</span> |
| <span class="identifier">InputIterator</span> <span class="identifier">b</span><span class="special">,</span> |
| <span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special"><</span><span class="identifier">InputIterator</span><span class="special">>::</span><span class="identifier">value_type</span> <span class="identifier">expected_mean</span><span class="special">);</span> |
| </pre> |
| <p> |
| Returns the probability that the data in the sequence [a,b) has the mean <span class="emphasis"><em>expected_mean</em></span>. |
| </p> |
| <h5> |
| <a name="math_toolkit.future.h3"></a> |
| <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 |
| With Statistical Accumulators</a> |
| </h5> |
| <p> |
| <a href="http://boost-sandbox.sourceforge.net/libs/accumulators/doc/html/index.html" target="_top">Eric |
| Niebler's accumulator framework</a> - also work in progress - provides |
| the means to calculate various statistical properties from experimental data. |
| There is an opportunity to integrate the statistical tests with this framework |
| at some later date: |
| </p> |
| <pre class="programlisting"><span class="comment">// Define an accumulator, all required statistics to calculate the test</span> |
| <span class="comment">// are calculated automatically:</span> |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">features</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">test_expected_mean</span><span class="special">></span> <span class="special">></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> |
| <span class="comment">// Pass our data to the accumulator:</span> |
| <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> |
| <span class="comment">// Extract the result:</span> |
| <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> |
| </pre> |
| </div> |
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| Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
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