# Boost C++ Libraries

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### boost/accumulators/statistics/skewness.hpp

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

#ifndef BOOST_ACCUMULATORS_STATISTICS_SKEWNESS_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_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/moment.hpp>
#include <boost/accumulators/statistics/mean.hpp>

namespace boost { namespace accumulators
{

namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// skewness_impl
/**
@brief Skewness estimation

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 3. 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.
*/
template<typename Sample>
struct skewness_impl
: accumulator_base
{
// for boost::result_of
typedef typename numeric::functional::fdiv<Sample, Sample>::result_type result_type;

skewness_impl(dont_care)
{
}

template<typename Args>
result_type result(Args const &args) const
{
return numeric::fdiv(
accumulators::moment<3>(args)
- 3. * accumulators::moment<2>(args) * mean(args)
+ 2. * mean(args) * mean(args) * mean(args)
, ( accumulators::moment<2>(args) - mean(args) * mean(args) )
* std::sqrt( accumulators::moment<2>(args) - mean(args) * mean(args) )
);
}

// serialization is done by accumulators it depends on
template<class Archive>
void serialize(Archive & ar, const unsigned int file_version) {}
};

} // namespace impl

///////////////////////////////////////////////////////////////////////////////
// tag::skewness
//
namespace tag
{
struct skewness
: depends_on<mean, moment<2>, moment<3> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::skewness_impl<mpl::_1> impl;
};
}

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

BOOST_ACCUMULATORS_IGNORE_GLOBAL(skewness)
}

using extract::skewness;

// So that skewness can be automatically substituted with
// weighted_skewness when the weight parameter is non-void
template<>
struct as_weighted_feature<tag::skewness>
{
typedef tag::weighted_skewness type;
};

template<>
struct feature_of<tag::weighted_skewness>
: feature_of<tag::skewness>
{
};

}} // namespace boost::accumulators

#endif