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Diffstat (limited to 'boost/accumulators/statistics/kurtosis.hpp')
-rw-r--r-- | boost/accumulators/statistics/kurtosis.hpp | 112 |
1 files changed, 112 insertions, 0 deletions
diff --git a/boost/accumulators/statistics/kurtosis.hpp b/boost/accumulators/statistics/kurtosis.hpp new file mode 100644 index 0000000000..4c5c23d5d7 --- /dev/null +++ b/boost/accumulators/statistics/kurtosis.hpp @@ -0,0 +1,112 @@ +/////////////////////////////////////////////////////////////////////////////// +// kurtosis.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_KURTOSIS_HPP_EAN_28_10_2005 +#define BOOST_ACCUMULATORS_STATISTICS_KURTOSIS_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/mean.hpp> +#include <boost/accumulators/statistics/moment.hpp> + +namespace boost { namespace accumulators +{ + +namespace impl +{ + /////////////////////////////////////////////////////////////////////////////// + // kurtosis_impl + /** + @brief Kurtosis estimation + + The kurtosis of a sample distribution is defined as the ratio of the 4th central moment and the square of the 2nd central + moment (the variance) of the samples, minus 3. The term \f$ -3 \f$ is added in order to ensure that the normal distribution + has zero kurtosis. The kurtosis can also be expressed by the simple moments: + + \f[ + \hat{g}_2 = + \frac + {\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} + {\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^2} - 3, + \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. + */ + template<typename Sample> + struct kurtosis_impl + : accumulator_base + { + // for boost::result_of + typedef typename numeric::functional::average<Sample, Sample>::result_type result_type; + + kurtosis_impl(dont_care) {} + + template<typename Args> + result_type result(Args const &args) const + { + return numeric::average( + accumulators::moment<4>(args) + - 4. * accumulators::moment<3>(args) * mean(args) + + 6. * accumulators::moment<2>(args) * mean(args) * mean(args) + - 3. * mean(args) * mean(args) * mean(args) * mean(args) + , ( accumulators::moment<2>(args) - mean(args) * mean(args) ) + * ( accumulators::moment<2>(args) - mean(args) * mean(args) ) + ) - 3.; + } + }; + +} // namespace impl + +/////////////////////////////////////////////////////////////////////////////// +// tag::kurtosis +// +namespace tag +{ + struct kurtosis + : depends_on<mean, moment<2>, moment<3>, moment<4> > + { + /// INTERNAL ONLY + /// + typedef accumulators::impl::kurtosis_impl<mpl::_1> impl; + }; +} + +/////////////////////////////////////////////////////////////////////////////// +// extract::kurtosis +// +namespace extract +{ + extractor<tag::kurtosis> const kurtosis = {}; + + BOOST_ACCUMULATORS_IGNORE_GLOBAL(kurtosis) +} + +using extract::kurtosis; + +// So that kurtosis can be automatically substituted with +// weighted_kurtosis when the weight parameter is non-void +template<> +struct as_weighted_feature<tag::kurtosis> +{ + typedef tag::weighted_kurtosis type; +}; + +template<> +struct feature_of<tag::weighted_kurtosis> + : feature_of<tag::kurtosis> +{ +}; + +}} // namespace boost::accumulators + +#endif |