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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.dist.future"></a><a class="link" href="future.html" title="Extras/Future Directions"> Extras/Future Directions</a>
</h3></div></div></div>
<a name="math_toolkit.dist.future.adding_additional_location_and_scale_parameters"></a><h5>
<a name="id1069435"></a>
<a class="link" href="future.html#math_toolkit.dist.future.adding_additional_location_and_scale_parameters">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>
<a name="math_toolkit.dist.future.an__quot_any_distribution_quot__class"></a><h5>
<a name="id1069600"></a>
<a class="link" href="future.html#math_toolkit.dist.future.an__quot_any_distribution_quot__class">An
"any_distribution" class</a>
</h5>
<p>
It would be fairly trivial 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. 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>
<a name="math_toolkit.dist.future.higher_level_hypothesis_tests"></a><h5>
<a name="id1069809"></a>
<a class="link" href="future.html#math_toolkit.dist.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>
<a name="math_toolkit.dist.future.integration_with_statistical_accumulators"></a><h5>
<a name="id1069971"></a>
<a class="link" href="future.html#math_toolkit.dist.future.integration_with_statistical_accumulators">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>
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and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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