/usr/include/boost/accumulators/statistics
Edit: /usr/include/boost/accumulators/statistics/kurtosis.hpp (3864B)
///////////////////////////////////////////////////////////////////////////////
// kurtosis.hpp
//
// Copyright 2006 Olivier Gygi, Daniel Egloff. 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)
#ifndef BOOST_ACCUMULATORS_STATISTICS_KURTOSIS_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_KURTOSIS_HPP_EAN_28_10_2005
#include
#include
#include
#include
#include
#include
#include
#include
#include
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// kurtosis_impl
/**
@brief Kurtosis estimation
The kurtosis of a sample distribution is defined as the ratio of the 4th central moment and the square of the 2nd central
moment (the variance) of the samples, minus 3. The term \f$ -3 \f$ is added in order to ensure that the normal distribution
has zero kurtosis. The kurtosis can also be expressed by the simple moments:
\f[
\hat{g}_2 =
\frac
{\widehat{m}_n^{(4)}-4\widehat{m}_n^{(3)}\hat{\mu}_n+6\widehat{m}_n^{(2)}\hat{\mu}_n^2-3\hat{\mu}_n^4}
{\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^2} - 3,
\f]
where \f$ \widehat{m}_n^{(i)} \f$ are the \f$ i \f$-th moment and \f$ \hat{\mu}_n \f$ the mean (first moment) of the
\f$ n \f$ samples.
*/
template
struct kurtosis_impl
: accumulator_base
{
// for boost::result_of
typedef typename numeric::functional::fdiv::result_type result_type;
kurtosis_impl(dont_care) {}
template
result_type result(Args const &args) const
{
return numeric::fdiv(
accumulators::moment<4>(args)
- 4. * accumulators::moment<3>(args) * mean(args)
+ 6. * accumulators::moment<2>(args) * mean(args) * mean(args)
- 3. * mean(args) * mean(args) * mean(args) * mean(args)
, ( accumulators::moment<2>(args) - mean(args) * mean(args) )
* ( accumulators::moment<2>(args) - mean(args) * mean(args) )
) - 3.;
}
// serialization is done by accumulators it depends on
template
void serialize(Archive & ar, const unsigned int file_version) {}
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::kurtosis
//
namespace tag
{
struct kurtosis
: depends_on, moment<3>, moment<4> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::kurtosis_impl impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::kurtosis
//
namespace extract
{
extractor const kurtosis = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(kurtosis)
}
using extract::kurtosis;
// So that kurtosis can be automatically substituted with
// weighted_kurtosis when the weight parameter is non-void
template<>
struct as_weighted_feature
{
typedef tag::weighted_kurtosis type;
};
template<>
struct feature_of
: feature_of
{
};
}} // namespace boost::accumulators
#endif