math/doc/dist_reference.qbk

[section:dist_ref Statistical Distributions Reference]

[def __cdf [link math.dist.cdf Cumulative Distribution Function]]
[def __pdf [link math.dist.pdf Probability Density Function]]
[def __ccdf [link math.dist.ccdf Complement of the Cumulative Distribution Function]]
[def __quantile [link math.dist.quantile Quantile]]
[def __quantile_c [link math.dist.quantile_c Quantile from the complement of the probability]]
[def __mean [link math.dist.mean mean]]
[def __mode [link math.dist.mode mode]]
[def __skewness [link math.dist.skewness skewness]]
[def __kurtosis [link math.dist.kurtosis kurtosis]]
[def __kurtosis_excess [link math.dist.kurtosis_excess kurtosis_excess]]
[def __variance [link math.dist.variance variance]]
[def __sd [link math.dist.sd standard deviation]]
[def __hazard [link math.dist.hazard Hazard Function]]
[def __chf [link math.dist.chf Cumulative Hazard Function]]

[/ def names end in distrib to avoid clashes]
[def __beta_distrib [link math_toolkit.dist.dist_ref.dists.beta_dist Beta Distribution]]
[def __binomial_distrib [link math_toolkit.dist.dist_ref.dists.binomial_dist Binomial Distribution]]
[def __negative_binomial_distrib [link math_toolkit.dist.dist_ref.dists.negative_binomial_dist Negative Binomial Distribution]]
[def __chi_squared_distrib [link math_toolkit.dist.dist_ref.dists.chi_squared_dist Chi Squared Distribution]]
[def __normal_distrib [link math_toolkit.dist.dist_ref.dists.normal_dist Normal Distribution]]
[def __F_distrib [link math_toolkit.dist.dist_ref.dists.f_dist Fisher F Distribution]]
[def __students_t_distrib [link math_toolkit.dist.dist_ref.dists.students_t_dist Students t Distribution]]

[def __usual_accessors __cdf, __pdf, __quantile, __hazard, 
   __chf, __mean, __mode, __variance, __sd, __skewness, __kurtosis and __kurtosis_excess]
   

[include distributions/non_members.qbk]

[section:dists Distributions]

[include distributions/beta.qbk]
[include distributions/binomial.qbk]
[include distributions/cauchy.qbk]
[include distributions/chi_squared.qbk]
[include distributions/exponential.qbk]
[include distributions/extreme_value.qbk]
[include distributions/fisher.qbk]
[include distributions/gamma.qbk]
[include distributions/lognormal.qbk]
[include distributions/negative_binomial.qbk]
[include distributions/normal.qbk]
[include distributions/poisson.qbk]
[include distributions/students_t.qbk]
[include distributions/weibull.qbk]

[endsect][/section:dists Distributions]

[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 would be fairly trivial to add a distribution object that virtualises
the actual type of the distibution, 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.  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 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).
]