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