...one of the most highly
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— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards

boost::accumulators::impl::kurtosis_impl — Kurtosis estimation.

// In header: <boost/accumulators/statistics/kurtosis.hpp> template<typename Sample> struct kurtosis_impl : public accumulator_base { // types typedef numeric::functional::fdiv< Sample, Sample >::result_type result_type; // construct/copy/destruct kurtosis_impl(dont_care); // public member functions template<typename Args> result_type result(Args const &) const; template<typename Archive> void serialize(Archive &, const unsigned int); };

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.