Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // skewness.hpp
Chris@16: //
Chris@16: //  Copyright 2006 Olivier Gygi, Daniel Egloff. Distributed under the Boost
Chris@16: //  Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_ACCUMULATORS_STATISTICS_SKEWNESS_HPP_EAN_28_10_2005
Chris@16: #define BOOST_ACCUMULATORS_STATISTICS_SKEWNESS_HPP_EAN_28_10_2005
Chris@16: 
Chris@16: #include <limits>
Chris@16: #include <boost/mpl/placeholders.hpp>
Chris@16: #include <boost/accumulators/framework/accumulator_base.hpp>
Chris@16: #include <boost/accumulators/framework/extractor.hpp>
Chris@16: #include <boost/accumulators/framework/parameters/sample.hpp>
Chris@16: #include <boost/accumulators/numeric/functional.hpp>
Chris@16: #include <boost/accumulators/framework/depends_on.hpp>
Chris@16: #include <boost/accumulators/statistics_fwd.hpp>
Chris@16: #include <boost/accumulators/statistics/moment.hpp>
Chris@16: #include <boost/accumulators/statistics/mean.hpp>
Chris@16: 
Chris@16: 
Chris@16: namespace boost { namespace accumulators
Chris@16: {
Chris@16: 
Chris@16: namespace impl
Chris@16: {
Chris@16:     ///////////////////////////////////////////////////////////////////////////////
Chris@16:     // skewness_impl
Chris@16:     /**
Chris@16:         @brief Skewness estimation
Chris@16: 
Chris@16:         The skewness of a sample distribution is defined as the ratio of the 3rd central moment and the \f$ 3/2 \f$-th power
Chris@16:         of the 2nd central moment (the variance) of the samples 3. The skewness can also be expressed by the simple moments:
Chris@16: 
Chris@16:         \f[
Chris@16:             \hat{g}_1 =
Chris@16:                 \frac
Chris@16:                 {\widehat{m}_n^{(3)}-3\widehat{m}_n^{(2)}\hat{\mu}_n+2\hat{\mu}_n^3}
Chris@16:                 {\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^{3/2}}
Chris@16:         \f]
Chris@16: 
Chris@16:         where \f$ \widehat{m}_n^{(i)} \f$ are the \f$ i \f$-th moment and \f$ \hat{\mu}_n \f$ the mean (first moment) of the
Chris@16:         \f$ n \f$ samples.
Chris@16:     */
Chris@16:     template<typename Sample>
Chris@16:     struct skewness_impl
Chris@16:       : accumulator_base
Chris@16:     {
Chris@16:         // for boost::result_of
Chris@16:         typedef typename numeric::functional::fdiv<Sample, Sample>::result_type result_type;
Chris@16: 
Chris@16:         skewness_impl(dont_care)
Chris@16:         {
Chris@16:         }
Chris@16: 
Chris@16:         template<typename Args>
Chris@16:         result_type result(Args const &args) const
Chris@16:         {
Chris@16:             return numeric::fdiv(
Chris@16:                         accumulators::moment<3>(args)
Chris@16:                         - 3. * accumulators::moment<2>(args) * mean(args)
Chris@16:                         + 2. * mean(args) * mean(args) * mean(args)
Chris@16:                       , ( accumulators::moment<2>(args) - mean(args) * mean(args) )
Chris@16:                         * std::sqrt( accumulators::moment<2>(args) - mean(args) * mean(args) )
Chris@16:                    );
Chris@16:         }
Chris@16:     };
Chris@16: 
Chris@16: } // namespace impl
Chris@16: 
Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // tag::skewness
Chris@16: //
Chris@16: namespace tag
Chris@16: {
Chris@16:     struct skewness
Chris@16:       : depends_on<mean, moment<2>, moment<3> >
Chris@16:     {
Chris@16:         /// INTERNAL ONLY
Chris@16:         ///
Chris@16:         typedef accumulators::impl::skewness_impl<mpl::_1> impl;
Chris@16:     };
Chris@16: }
Chris@16: 
Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // extract::skewness
Chris@16: //
Chris@16: namespace extract
Chris@16: {
Chris@16:     extractor<tag::skewness> const skewness = {};
Chris@16: 
Chris@16:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(skewness)
Chris@16: }
Chris@16: 
Chris@16: using extract::skewness;
Chris@16: 
Chris@16: // So that skewness can be automatically substituted with
Chris@16: // weighted_skewness when the weight parameter is non-void
Chris@16: template<>
Chris@16: struct as_weighted_feature<tag::skewness>
Chris@16: {
Chris@16:     typedef tag::weighted_skewness type;
Chris@16: };
Chris@16: 
Chris@16: template<>
Chris@16: struct feature_of<tag::weighted_skewness>
Chris@16:   : feature_of<tag::skewness>
Chris@16: {
Chris@16: };
Chris@16: 
Chris@16: }} // namespace boost::accumulators
Chris@16: 
Chris@16: #endif