/////////////////////////////////////////////////////////////////////////////// | |
// kurtosis.hpp | |
// | |
// Copyright 2006 Olivier Gygi, Daniel Egloff. Distributed under the Boost | |
// Software License, Version 1.0. (See accompanying file | |
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) | |
#ifndef BOOST_ACCUMULATORS_STATISTICS_KURTOSIS_HPP_EAN_28_10_2005 | |
#define BOOST_ACCUMULATORS_STATISTICS_KURTOSIS_HPP_EAN_28_10_2005 | |
#include <limits> | |
#include <boost/mpl/placeholders.hpp> | |
#include <boost/accumulators/framework/accumulator_base.hpp> | |
#include <boost/accumulators/framework/extractor.hpp> | |
#include <boost/accumulators/framework/parameters/sample.hpp> | |
#include <boost/accumulators/numeric/functional.hpp> | |
#include <boost/accumulators/framework/depends_on.hpp> | |
#include <boost/accumulators/statistics/mean.hpp> | |
#include <boost/accumulators/statistics/moment.hpp> | |
namespace boost { namespace accumulators | |
{ | |
namespace impl | |
{ | |
/////////////////////////////////////////////////////////////////////////////// | |
// kurtosis_impl | |
/** | |
@brief 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 \f$ -3 \f$ is added in order to ensure that the normal distribution | |
has zero kurtosis. The kurtosis can also be expressed by the simple moments: | |
\f[ | |
\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, | |
\f] | |
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 | |
\f$ n \f$ samples. | |
*/ | |
template<typename Sample> | |
struct kurtosis_impl | |
: accumulator_base | |
{ | |
// for boost::result_of | |
typedef typename numeric::functional::average<Sample, Sample>::result_type result_type; | |
kurtosis_impl(dont_care) {} | |
template<typename Args> | |
result_type result(Args const &args) const | |
{ | |
return numeric::average( | |
accumulators::moment<4>(args) | |
- 4. * accumulators::moment<3>(args) * mean(args) | |
+ 6. * accumulators::moment<2>(args) * mean(args) * mean(args) | |
- 3. * mean(args) * mean(args) * mean(args) * mean(args) | |
, ( accumulators::moment<2>(args) - mean(args) * mean(args) ) | |
* ( accumulators::moment<2>(args) - mean(args) * mean(args) ) | |
) - 3.; | |
} | |
}; | |
} // namespace impl | |
/////////////////////////////////////////////////////////////////////////////// | |
// tag::kurtosis | |
// | |
namespace tag | |
{ | |
struct kurtosis | |
: depends_on<mean, moment<2>, moment<3>, moment<4> > | |
{ | |
/// INTERNAL ONLY | |
/// | |
typedef accumulators::impl::kurtosis_impl<mpl::_1> impl; | |
}; | |
} | |
/////////////////////////////////////////////////////////////////////////////// | |
// extract::kurtosis | |
// | |
namespace extract | |
{ | |
extractor<tag::kurtosis> const kurtosis = {}; | |
BOOST_ACCUMULATORS_IGNORE_GLOBAL(kurtosis) | |
} | |
using extract::kurtosis; | |
// So that kurtosis can be automatically substituted with | |
// weighted_kurtosis when the weight parameter is non-void | |
template<> | |
struct as_weighted_feature<tag::kurtosis> | |
{ | |
typedef tag::weighted_kurtosis type; | |
}; | |
template<> | |
struct feature_of<tag::weighted_kurtosis> | |
: feature_of<tag::kurtosis> | |
{ | |
}; | |
}} // namespace boost::accumulators | |
#endif |