141 lines
4.5 KiB
Plaintext
141 lines
4.5 KiB
Plaintext
[section:dist_ref Statistical Distributions Reference]
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[include non_members.qbk]
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[section:dists Distributions]
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[include arcsine.qbk]
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[include bernoulli.qbk]
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[include beta.qbk]
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[include binomial.qbk]
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[include cauchy.qbk]
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[include chi_squared.qbk]
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[include empirical_cdf.qbk]
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[include exponential.qbk]
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[include extreme_value.qbk]
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[include fisher.qbk]
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[include gamma.qbk]
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[include geometric.qbk]
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[include hyperexponential.qbk]
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[include hypergeometric.qbk]
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[include inverse_chi_squared.qbk]
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[include inverse_gamma.qbk]
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[include inverse_gaussian.qbk]
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[include laplace.qbk]
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[include logistic.qbk]
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[include lognormal.qbk]
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[include negative_binomial.qbk]
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[include nc_beta.qbk]
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[include nc_chi_squared.qbk]
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[include nc_f.qbk]
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[include nc_t.qbk]
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[include normal.qbk]
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[include pareto.qbk]
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[include poisson.qbk]
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[include rayleigh.qbk]
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[include skew_normal.qbk]
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[include students_t.qbk]
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[include triangular.qbk]
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[include uniform.qbk]
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[include weibull.qbk]
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[endsect] [/section:dists Distributions]
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[include dist_algorithms.qbk]
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[endsect] [/section:dist_ref Statistical Distributions and Functions Reference]
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[section:future Extras/Future Directions]
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[h4 Adding Additional Location and Scale Parameters]
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In some modelling applications we require a distribution
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with a specific location and scale:
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often this equates to a specific mean and standard deviation, although for many
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distributions the relationship between these properties and the location and
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scale parameters are non-trivial. See
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[@http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm]
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for more information.
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The obvious way to handle this is via an adapter template:
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template <class Dist>
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class scaled_distribution
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{
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scaled_distribution(
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const Dist dist,
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typename Dist::value_type location,
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typename Dist::value_type scale = 0);
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};
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Which would then have its own set of overloads for the non-member accessor functions.
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[h4 An "any_distribution" class]
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It is easy to add a distribution object that virtualises
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the actual type of the distribution, and can therefore hold "any" object
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that conforms to the conceptual requirements of a distribution:
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template <class RealType>
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class any_distribution
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{
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public:
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template <class Distribution>
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any_distribution(const Distribution& d);
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};
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// Get the cdf of the underlying distribution:
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template <class RealType>
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RealType cdf(const any_distribution<RealType>& d, RealType x);
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// etc....
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Such a class would facilitate the writing of non-template code that can
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function with any distribution type.
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The [@http://sourceforge.net/projects/distexplorer/ Statistical Distribution Explorer]
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utility for Windows is a usage example.
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It's not clear yet whether there is a compelling use case though.
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Possibly tests for goodness of fit might
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provide such a use case: this needs more investigation.
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[h4 Higher Level Hypothesis Tests]
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Higher-level tests roughly corresponding to the
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[@http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/Statistics/HypothesisTests.html Mathematica Hypothesis Tests]
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package could be added reasonably easily, for example:
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template <class InputIterator>
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typename std::iterator_traits<InputIterator>::value_type
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test_equal_mean(
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InputIterator a,
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InputIterator b,
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typename std::iterator_traits<InputIterator>::value_type expected_mean);
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Returns the probability that the data in the sequence \[a,b) has the mean
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/expected_mean/.
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[h4 Integration With Statistical Accumulators]
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[@http://boost-sandbox.sourceforge.net/libs/accumulators/doc/html/index.html
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Eric Niebler's accumulator framework] - also work in progress - provides the means
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to calculate various statistical properties from experimental data. There is an
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opportunity to integrate the statistical tests with this framework at some later date:
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// Define an accumulator, all required statistics to calculate the test
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// are calculated automatically:
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accumulator_set<double, features<tag::test_expected_mean> > acc(expected_mean=4);
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// Pass our data to the accumulator:
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acc = std::for_each(mydata.begin(), mydata.end(), acc);
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// Extract the result:
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double p = probability(acc);
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[endsect] [/section:future Extras Future Directions]
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[/ dist_reference.qbk
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Copyright 2006, 2010 John Maddock and Paul A. Bristow.
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt).
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]
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