Kurtosis estimation. More...

#include <statistics_fwd.hpp>

Inheritance diagram for boost::accumulators::impl::kurtosis_impl< Sample >:

Collaboration diagram for boost::accumulators::impl::kurtosis_impl< Sample >:

Public Types
typedef numeric::functional::fdiv < Sample, Sample > ::result_type	result_type

typedef mpl::false_	is_droppable

Public Member Functions
	kurtosis_impl (dont_care)

template<typename Args >
result_type	result (Args const &args) const

detail::void_	operator() (dont_care)

detail::void_	add_ref (dont_care)

detail::void_	drop (dont_care)

detail::void_	on_drop (dont_care)

Detailed Description

template<typename Sample>
struct boost::accumulators::impl::kurtosis_impl< Sample >

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 $ -3 $ is added in order to ensure that the normal distribution has zero kurtosis. The kurtosis can also be expressed by the simple moments:

$\hat{g}_2 = \frac {\widehat{m}_n^{(4)}-4\widehat{m}_n^{(3)}\hat{\mu}_n+6\widehat{m}_n^{(2)}\hat{\mu}_n^2-3\hat{\mu}_n^4} {\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^2} - 3,$