/////////////////////////////////////////////////////////////////////////////// // 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