ceph/src/boost/libs/math/doc/distributions/dist_reference.qbk

   1 [section:dist_ref Statistical Distributions Reference]
   2
   3 [include non_members.qbk]
   4
   5 [section:dists Distributions]
   6
   7 [include arcsine.qbk]
   8 [include bernoulli.qbk]
   9 [include beta.qbk]
  10 [include binomial.qbk]
  11 [include cauchy.qbk]
  12 [include chi_squared.qbk]
  13 [include exponential.qbk]
  14 [include extreme_value.qbk]
  15 [include fisher.qbk]
  16 [include gamma.qbk]
  17 [include geometric.qbk]
  18 [include hyperexponential.qbk]
  19 [include hypergeometric.qbk]
  20 [include inverse_chi_squared.qbk]
  21 [include inverse_gamma.qbk]
  22 [include inverse_gaussian.qbk]
  23 [include laplace.qbk]
  24 [include logistic.qbk]
  25 [include lognormal.qbk]
  26 [include negative_binomial.qbk]
  27 [include nc_beta.qbk]
  28 [include nc_chi_squared.qbk]
  29 [include nc_f.qbk]
  30 [include nc_t.qbk]
  31 [include normal.qbk]
  32 [include pareto.qbk]
  33 [include poisson.qbk]
  34 [include rayleigh.qbk]
  35 [include skew_normal.qbk]
  36 [include students_t.qbk]
  37 [include triangular.qbk]
  38 [include uniform.qbk]
  39 [include weibull.qbk]
  40
  41 [endsect] [/section:dists Distributions]
  42
  43 [include dist_algorithms.qbk]
  44
  45 [endsect] [/section:dist_ref Statistical Distributions and Functions Reference]
  46
  47
  48 [section:future Extras/Future Directions]
  49
  50 [h4 Adding Additional Location and Scale Parameters]
  51
  52 In some modelling applications we require a distribution
  53 with a specific location and scale:
  54 often this equates to a specific mean and standard deviation, although for many
  55 distributions the relationship between these properties and the location and
  56 scale parameters are non-trivial. See
  57 [@http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm]
  58 for more information.
  59
  60 The obvious way to handle this is via an adapter template:
  61
  62   template <class Dist>
  63   class scaled_distribution
  64   {
  65      scaled_distribution(
  66        const Dist dist,
  67        typename Dist::value_type location,
  68        typename Dist::value_type scale = 0);
  69   };
  70
  71 Which would then have its own set of overloads for the non-member accessor functions.
  72
  73 [h4 An "any_distribution" class]
  74
  75 It is easy to add a distribution object that virtualises
  76 the actual type of the distribution, and can therefore hold "any" object
  77 that conforms to the conceptual requirements of a distribution:
  78
  79    template <class RealType>
  80    class any_distribution
  81    {
  82    public:
  83       template <class Distribution>
  84       any_distribution(const Distribution& d);
  85    };
  86
  87    // Get the cdf of the underlying distribution:
  88    template <class RealType>
  89    RealType cdf(const any_distribution<RealType>& d, RealType x);
  90    // etc....
  91
  92 Such a class would facilitate the writing of non-template code that can
  93 function with any distribution type.
  94
  95 The [@http://sourceforge.net/projects/distexplorer/ Statistical Distribution Explorer]
  96 utility for Windows is a usage example.
  97
  98 It's not clear yet whether there is a compelling use case though.
  99 Possibly tests for goodness of fit might
 100 provide such a use case: this needs more investigation.
 101
 102 [h4 Higher Level Hypothesis Tests]
 103
 104 Higher-level tests roughly corresponding to the
 105 [@http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/Statistics/HypothesisTests.html Mathematica Hypothesis Tests]
 106 package could be added reasonably easily, for example:
 107
 108   template <class InputIterator>
 109   typename std::iterator_traits<InputIterator>::value_type
 110      test_equal_mean(
 111        InputIterator a,
 112        InputIterator b,
 113        typename std::iterator_traits<InputIterator>::value_type expected_mean);
 114
 115 Returns the probability that the data in the sequence \[a,b) has the mean
 116 /expected_mean/.
 117
 118 [h4 Integration With Statistical Accumulators]
 119
 120 [@http://boost-sandbox.sourceforge.net/libs/accumulators/doc/html/index.html
 121 Eric Niebler's accumulator framework] - also work in progress - provides the means
 122 to calculate various statistical properties from experimental data.  There is an
 123 opportunity to integrate the statistical tests with this framework at some later date:
 124
 125   // Define an accumulator, all required statistics to calculate the test
 126   // are calculated automatically:
 127   accumulator_set<double, features<tag::test_expected_mean> > acc(expected_mean=4);
 128   // Pass our data to the accumulator:
 129   acc = std::for_each(mydata.begin(), mydata.end(), acc);
 130   // Extract the result:
 131   double p = probability(acc);
 132
 133 [endsect] [/section:future Extras Future Directions]
 134
 135 [/ dist_reference.qbk
 136   Copyright 2006, 2010 John Maddock and Paul A. Bristow.
 137   Distributed under the Boost Software License, Version 1.0.
 138   (See accompanying file LICENSE_1_0.txt or copy at
 139   http://www.boost.org/LICENSE_1_0.txt).
 140 ]
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