/////////////////////////////////////////////////////////////////////////////// | |
// skewness.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_SKEWNESS_HPP_EAN_28_10_2005 | |
#define BOOST_ACCUMULATORS_STATISTICS_SKEWNESS_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_fwd.hpp> | |
#include <boost/accumulators/statistics/moment.hpp> | |
#include <boost/accumulators/statistics/mean.hpp> | |
namespace boost { namespace accumulators | |
{ | |
namespace impl | |
{ | |
/////////////////////////////////////////////////////////////////////////////// | |
// skewness_impl | |
/** | |
@brief Skewness estimation | |
The skewness of a sample distribution is defined as the ratio of the 3rd central moment and the \f$ 3/2 \f$-th power | |
of the 2nd central moment (the variance) of the sampless 3. The skewness can also be expressed by the simple moments: | |
\f[ | |
\hat{g}_1 = | |
\frac | |
{\widehat{m}_n^{(3)}-3\widehat{m}_n^{(2)}\hat{\mu}_n+2\hat{\mu}_n^3} | |
{\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^{3/2}} | |
\f] | |
where \f$ \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 skewness_impl | |
: accumulator_base | |
{ | |
// for boost::result_of | |
typedef typename numeric::functional::average<Sample, Sample>::result_type result_type; | |
skewness_impl(dont_care) | |
{ | |
} | |
template<typename Args> | |
result_type result(Args const &args) const | |
{ | |
return numeric::average( | |
accumulators::moment<3>(args) | |
- 3. * accumulators::moment<2>(args) * mean(args) | |
+ 2. * mean(args) * mean(args) * mean(args) | |
, ( accumulators::moment<2>(args) - mean(args) * mean(args) ) | |
* std::sqrt( accumulators::moment<2>(args) - mean(args) * mean(args) ) | |
); | |
} | |
}; | |
} // namespace impl | |
/////////////////////////////////////////////////////////////////////////////// | |
// tag::skewness | |
// | |
namespace tag | |
{ | |
struct skewness | |
: depends_on<mean, moment<2>, moment<3> > | |
{ | |
/// INTERNAL ONLY | |
/// | |
typedef accumulators::impl::skewness_impl<mpl::_1> impl; | |
}; | |
} | |
/////////////////////////////////////////////////////////////////////////////// | |
// extract::skewness | |
// | |
namespace extract | |
{ | |
extractor<tag::skewness> const skewness = {}; | |
BOOST_ACCUMULATORS_IGNORE_GLOBAL(skewness) | |
} | |
using extract::skewness; | |
// So that skewness can be automatically substituted with | |
// weighted_skewness when the weight parameter is non-void | |
template<> | |
struct as_weighted_feature<tag::skewness> | |
{ | |
typedef tag::weighted_skewness type; | |
}; | |
template<> | |
struct feature_of<tag::weighted_skewness> | |
: feature_of<tag::skewness> | |
{ | |
}; | |
}} // namespace boost::accumulators | |
#endif |