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boost/accumulators/statistics/weighted_skewness.hpp

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

#ifndef BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_SKEWNESS_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_SKEWNESS_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_skewness_impl
/**
@brief Skewness estimation for weighted samples

The skewness of a sample distribution is defined as the ratio of the 3rd central moment and the \f$3/2 \f$-th power $of the 2nd central moment (the variance) of the samples. The skewness can also be expressed by the simple moments: \f[ \hat{g}_1 = \frac {\widehat{m}_n^{(3)}-3\widehat{m}_n^{(2)}\hat{\mu}_n+2\hat{\mu}_n^3} {\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^{3/2}} \f] where \f$ \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 skewness 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_skewness_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
// for boost::result_of
typedef typename numeric::functional::average<weighted_sample, weighted_sample>::result_type result_type;

weighted_skewness_impl(dont_care) {}

template<typename Args>
result_type result(Args const &args) const
{
return numeric::average(
weighted_moment<3>(args)
- 3. * weighted_moment<2>(args) * weighted_mean(args)
+ 2. * weighted_mean(args) * weighted_mean(args) * weighted_mean(args)
, ( weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) )
* std::sqrt( weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) )
);
}
};

} // namespace impl

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

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

using extract::weighted_skewness;

}} // namespace boost::accumulators

#endif