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boost/accumulators/statistics/weighted_kurtosis.hpp

///////////////////////////////////////////////////////////////////////////////
// weighted_kurtosis.hpp
//
//  Software License, Version 1.0. (See accompanying file

#ifndef BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_KURTOSIS_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_KURTOSIS_HPP_EAN_28_10_2005

#include <limits>
#include <boost/mpl/placeholders.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/weighted_moment.hpp>
#include <boost/accumulators/statistics/weighted_mean.hpp>

namespace boost { namespace accumulators
{

namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// weighted_kurtosis_impl
/**
@brief Kurtosis estimation for weighted samples

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.

The kurtosis estimator for weighted samples is formally identical to the estimator for unweighted samples, except that
the weighted counterparts of all measures it depends on are to be taken.
*/
template<typename Sample, typename Weight>
struct weighted_kurtosis_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
// for boost::result_of
typedef typename numeric::functional::fdiv<weighted_sample, weighted_sample>::result_type result_type;

weighted_kurtosis_impl(dont_care)
{
}

template<typename Args>
result_type result(Args const &args) const
{
return numeric::fdiv(
accumulators::weighted_moment<4>(args)
- 4. * accumulators::weighted_moment<3>(args) * weighted_mean(args)
+ 6. * accumulators::weighted_moment<2>(args) * weighted_mean(args) * weighted_mean(args)
- 3. * weighted_mean(args) * weighted_mean(args) * weighted_mean(args) * weighted_mean(args)
, ( accumulators::weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) )
* ( accumulators::weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) )
) - 3.;
}
};

} // namespace impl

///////////////////////////////////////////////////////////////////////////////
// tag::weighted_kurtosis
//
namespace tag
{
struct weighted_kurtosis
: depends_on<weighted_mean, weighted_moment<2>, weighted_moment<3>, weighted_moment<4> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::weighted_kurtosis_impl<mpl::_1, mpl::_2> impl;
};
}

///////////////////////////////////////////////////////////////////////////////
// extract::weighted_kurtosis
//
namespace extract
{
extractor<tag::weighted_kurtosis> const weighted_kurtosis = {};

BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_kurtosis)
}

using extract::weighted_kurtosis;

}} // namespace boost::accumulators

#endif