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[section:dist_ref Statistical Distributions Reference]
[include non_members.qbk]
[section:dists Distributions]
[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).
]
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