[ceph.git] / ceph / src / boost / libs / math / doc / distributions / dist_reference.qbk

[section:dist_ref Statistical Distributions Reference]

[include non_members.qbk]

[section:dists Distributions]

[include arcsine.qbk]
[include bernoulli.qbk]
[include beta.qbk]
[include binomial.qbk]
[include cauchy.qbk]
[include chi_squared.qbk]
[include exponential.qbk]
[include extreme_value.qbk]
[include fisher.qbk]
[include gamma.qbk]
[include geometric.qbk]
[include hyperexponential.qbk]
[include hypergeometric.qbk]
[include inverse_chi_squared.qbk]
[include inverse_gamma.qbk]
[include inverse_gaussian.qbk]
[include laplace.qbk]
[include logistic.qbk]
[include lognormal.qbk]
[include negative_binomial.qbk]
[include nc_beta.qbk]
[include nc_chi_squared.qbk]
[include nc_f.qbk]
[include nc_t.qbk]
[include normal.qbk]
[include pareto.qbk]
[include poisson.qbk]
[include rayleigh.qbk]
[include skew_normal.qbk]
[include students_t.qbk]
[include triangular.qbk]
[include uniform.qbk]
[include weibull.qbk]

[endsect] [/section:dists Distributions]

[include dist_algorithms.qbk]

[endsect] [/section:dist_ref Statistical Distributions and Functions Reference]


[section:future Extras/Future Directions]

[h4 Adding Additional Location and Scale Parameters]

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
[@http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm]
for more information.

The obvious way to handle this is via an adapter template:

  template <class Dist>
  class scaled_distribution
  {
     scaled_distribution(
       const Dist dist,
       typename Dist::value_type location,
       typename Dist::value_type scale = 0);
  };

Which would then have its own set of overloads for the non-member accessor functions.

[h4 An "any_distribution" class]

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:

   template <class RealType>
   class any_distribution
   {
   public:
      template <class Distribution>
      any_distribution(const Distribution& d);
   };

   // Get the cdf of the underlying distribution:
   template <class RealType>
   RealType cdf(const any_distribution<RealType>& d, RealType x);
   // etc....

Such a class would facilitate the writing of non-template code that can
function with any distribution type.

The [@http://sourceforge.net/projects/distexplorer/ Statistical Distribution Explorer]
utility for Windows is a usage example.

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.

[h4 Higher Level Hypothesis Tests]

Higher-level tests roughly corresponding to the
[@http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/Statistics/HypothesisTests.html Mathematica Hypothesis Tests]
package could be added reasonably easily, for example:

  template <class InputIterator>
  typename std::iterator_traits<InputIterator>::value_type
     test_equal_mean(
       InputIterator a,
       InputIterator b,
       typename std::iterator_traits<InputIterator>::value_type expected_mean);

Returns the probability that the data in the sequence \[a,b) has the mean
/expected_mean/.

[h4 Integration With Statistical Accumulators]

[@http://boost-sandbox.sourceforge.net/libs/accumulators/doc/html/index.html
Eric Niebler's accumulator framework] - 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:

  // Define an accumulator, all required statistics to calculate the test
  // are calculated automatically:
  accumulator_set<double, features<tag::test_expected_mean> > acc(expected_mean=4);
  // Pass our data to the accumulator:
  acc = std::for_each(mydata.begin(), mydata.end(), acc);
  // Extract the result:
  double p = probability(acc);

[endsect] [/section:future Extras Future Directions]

[/ dist_reference.qbk
  Copyright 2006, 2010 John Maddock and Paul A. Bristow.
  Distributed under the Boost Software License, Version 1.0.
  (See accompanying file LICENSE_1_0.txt or copy at
  http://www.boost.org/LICENSE_1_0.txt).
]
Commit	Line	Data
7c673cae FG	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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