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boost::accumulators::impl::weighted_kurtosis_impl — Kurtosis estimation for weighted samples.
// In header: <boost/accumulators/statistics_fwd.hpp> template<typename Sample, typename Weight> struct weighted_kurtosis_impl : public accumulator_base { // 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:
 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
 are the  -th moment and
-th moment and  the mean (first moment) of the
 the mean (first moment) of the  samples.
 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.