mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2025-11-03 21:40:52 -05:00
148 lines
4.4 KiB
Plaintext
148 lines
4.4 KiB
Plaintext
[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).
|
|
]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|