Imported existing code

libraries/include/boost/accumulators/statistics/weighted_kurtosis.hpp

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+///////////////////////////////////////////////////////////////////////////////
+// weighted_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_WEIGHTED_KURTOSIS_HPP_EAN_28_10_2005
+#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_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_fwd.hpp>
+#include <boost/accumulators/statistics/weighted_moment.hpp>
+#include <boost/accumulators/statistics/weighted_mean.hpp>
+
+namespace boost { namespace accumulators
+{
+
+namespace impl
+{
+    ///////////////////////////////////////////////////////////////////////////////
+    // weighted_kurtosis_impl
+    /**
+        @brief Kurtosis estimation for weighted samples
+
+        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.
+
+        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.
+    */
+    template<typename Sample, typename Weight>
+    struct weighted_kurtosis_impl
+      : accumulator_base
+    {
+        typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
+        // for boost::result_of
+        typedef typename numeric::functional::average<weighted_sample, weighted_sample>::result_type result_type;
+
+        weighted_kurtosis_impl(dont_care)
+        {
+        }
+
+        template<typename Args>
+        result_type result(Args const &args) const
+        {
+            return numeric::average(
+                        weighted_moment<4>(args)
+                        - 4. * weighted_moment<3>(args) * weighted_mean(args)
+                        + 6. * weighted_moment<2>(args) * weighted_mean(args) * weighted_mean(args)
+                        - 3. * weighted_mean(args) * weighted_mean(args) * weighted_mean(args) * weighted_mean(args)
+                      , ( weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) )
+                        * ( weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) )
+                   ) - 3.;
+        }
+    };
+
+} // namespace impl
+
+///////////////////////////////////////////////////////////////////////////////
+// tag::weighted_kurtosis
+//
+namespace tag
+{
+    struct weighted_kurtosis
+      : depends_on<weighted_mean, weighted_moment<2>, weighted_moment<3>, weighted_moment<4> >
+    {
+        /// INTERNAL ONLY
+        ///
+        typedef accumulators::impl::weighted_kurtosis_impl<mpl::_1, mpl::_2> impl;
+    };
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// extract::weighted_kurtosis
+//
+namespace extract
+{
+    extractor<tag::weighted_kurtosis> const weighted_kurtosis = {};
+}
+
+using extract::weighted_kurtosis;
+
+}} // namespace boost::accumulators
+
+#endif