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101 lines
3.8 KiB
101 lines
3.8 KiB
/////////////////////////////////////////////////////////////////////////////// |
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// weighted_skewness.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_SKEWNESS_HPP_EAN_28_10_2005 |
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#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_SKEWNESS_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_skewness_impl |
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/** |
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@brief Skewness estimation for weighted samples |
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The skewness of a sample distribution is defined as the ratio of the 3rd central moment and the \f$ 3/2 \f$-th power $ |
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of the 2nd central moment (the variance) of the samples. The skewness can also be expressed by the simple moments: |
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\f[ |
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\hat{g}_1 = |
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\frac |
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{\widehat{m}_n^{(3)}-3\widehat{m}_n^{(2)}\hat{\mu}_n+2\hat{\mu}_n^3} |
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{\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^{3/2}} |
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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 skewness 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_skewness_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::average<weighted_sample, weighted_sample>::result_type result_type; |
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weighted_skewness_impl(dont_care) {} |
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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::average( |
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accumulators::weighted_moment<3>(args) |
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- 3. * accumulators::weighted_moment<2>(args) * weighted_mean(args) |
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+ 2. * 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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* std::sqrt( accumulators::weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) ) |
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); |
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} |
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}; |
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} // namespace impl |
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/////////////////////////////////////////////////////////////////////////////// |
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// tag::weighted_skewness |
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// |
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namespace tag |
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{ |
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struct weighted_skewness |
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: depends_on<weighted_mean, weighted_moment<2>, weighted_moment<3> > |
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{ |
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/// INTERNAL ONLY |
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/// |
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typedef accumulators::impl::weighted_skewness_impl<mpl::_1, mpl::_2> impl; |
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}; |
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} |
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/////////////////////////////////////////////////////////////////////////////// |
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// extract::weighted_skewness |
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// |
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namespace extract |
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{ |
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extractor<tag::weighted_skewness> const weighted_skewness = {}; |
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BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_skewness) |
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} |
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using extract::weighted_skewness; |
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}} // namespace boost::accumulators |
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#endif
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