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Diffstat (limited to 'boost/accumulators/statistics/weighted_skewness.hpp')
-rw-r--r-- | boost/accumulators/statistics/weighted_skewness.hpp | 101 |
1 files changed, 101 insertions, 0 deletions
diff --git a/boost/accumulators/statistics/weighted_skewness.hpp b/boost/accumulators/statistics/weighted_skewness.hpp new file mode 100644 index 0000000000..6ccbc45ca1 --- /dev/null +++ b/boost/accumulators/statistics/weighted_skewness.hpp @@ -0,0 +1,101 @@ +/////////////////////////////////////////////////////////////////////////////// +// 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::average<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::average( + 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 |