106 lines
4.0 KiB
C++
106 lines
4.0 KiB
C++
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///////////////////////////////////////////////////////////////////////////////
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// weighted_kurtosis.hpp
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//
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// Copyright 2006 Olivier Gygi, Daniel Egloff. Distributed under the Boost
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// Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_KURTOSIS_HPP_EAN_28_10_2005
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#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_KURTOSIS_HPP_EAN_28_10_2005
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#include <limits>
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#include <boost/mpl/placeholders.hpp>
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#include <boost/accumulators/framework/accumulator_base.hpp>
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#include <boost/accumulators/framework/extractor.hpp>
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#include <boost/accumulators/framework/parameters/sample.hpp>
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#include <boost/accumulators/numeric/functional.hpp>
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#include <boost/accumulators/framework/depends_on.hpp>
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#include <boost/accumulators/statistics_fwd.hpp>
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#include <boost/accumulators/statistics/weighted_moment.hpp>
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#include <boost/accumulators/statistics/weighted_mean.hpp>
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namespace boost { namespace accumulators
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{
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namespace impl
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{
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///////////////////////////////////////////////////////////////////////////////
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// weighted_kurtosis_impl
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/**
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@brief Kurtosis estimation for weighted samples
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The kurtosis of a sample distribution is defined as the ratio of the 4th central moment and the square of the 2nd central
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moment (the variance) of the samples, minus 3. The term \f$ -3 \f$ is added in order to ensure that the normal distribution
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has zero kurtosis. The kurtosis can also be expressed by the simple moments:
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\f[
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\hat{g}_2 =
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\frac
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{\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}
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{\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^2} - 3,
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\f]
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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
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\f$ n \f$ samples.
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The kurtosis estimator for weighted samples is formally identical to the estimator for unweighted samples, except that
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the weighted counterparts of all measures it depends on are to be taken.
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*/
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template<typename Sample, typename Weight>
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struct weighted_kurtosis_impl
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: accumulator_base
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{
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typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
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// for boost::result_of
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typedef typename numeric::functional::fdiv<weighted_sample, weighted_sample>::result_type result_type;
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weighted_kurtosis_impl(dont_care)
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{
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}
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template<typename Args>
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result_type result(Args const &args) const
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{
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return numeric::fdiv(
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accumulators::weighted_moment<4>(args)
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- 4. * accumulators::weighted_moment<3>(args) * weighted_mean(args)
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+ 6. * accumulators::weighted_moment<2>(args) * weighted_mean(args) * weighted_mean(args)
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- 3. * weighted_mean(args) * weighted_mean(args) * weighted_mean(args) * weighted_mean(args)
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, ( accumulators::weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) )
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* ( accumulators::weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) )
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) - 3.;
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}
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};
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} // namespace impl
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///////////////////////////////////////////////////////////////////////////////
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// tag::weighted_kurtosis
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//
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namespace tag
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{
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struct weighted_kurtosis
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: depends_on<weighted_mean, weighted_moment<2>, weighted_moment<3>, weighted_moment<4> >
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{
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/// INTERNAL ONLY
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///
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typedef accumulators::impl::weighted_kurtosis_impl<mpl::_1, mpl::_2> impl;
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};
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}
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///////////////////////////////////////////////////////////////////////////////
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// extract::weighted_kurtosis
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//
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namespace extract
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{
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extractor<tag::weighted_kurtosis> const weighted_kurtosis = {};
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BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_kurtosis)
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}
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using extract::weighted_kurtosis;
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}} // namespace boost::accumulators
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#endif
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