boost/accumulators/statistics/weighted_skewness.hpp
///////////////////////////////////////////////////////////////////////////////
// weighted_skewness.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_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::fdiv<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::fdiv(
accumulators::weighted_moment<3>(args)
- 3. * accumulators::weighted_moment<2>(args) * weighted_mean(args)
+ 2. * weighted_mean(args) * weighted_mean(args) * weighted_mean(args)
, ( accumulators::weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) )
* std::sqrt( accumulators::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 = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_skewness)
}
using extract::weighted_skewness;
}} // namespace boost::accumulators
#endif