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boost::accumulators::impl::weighted_kurtosis_impl — Kurtosis estimation for weighted samples.

// In header: <boost/accumulators/statistics/weighted_kurtosis.hpp> template<typename Sample, typename Weight> struct weighted_kurtosis_impl : public accumulator_base { // types typedef numeric::functional::multiplies< Sample, Weight >::result_type weighted_sample; typedef numeric::functional::fdiv< weighted_sample, weighted_sample >::result_type result_type; // construct/copy/destruct weighted_kurtosis_impl(dont_care); // public member functions template<typename Args> result_type result(Args const &) const; };

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 is added in order to ensure that the normal distribution has zero kurtosis. The kurtosis can also be expressed by the simple moments:

where are the -th moment and the mean (first moment) of the samples.

The kurtosis 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.