/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*

 Copyright (C) 2003 Ferdinando Ametrano

 Copyright (C) 2003 RiskMap srl

 This file is part of QuantLib, a free-software/open-source library

 for financial quantitative analysts and developers - http://quantlib.org/

 QuantLib is free software: you can redistribute it and/or modify it

 under the terms of the QuantLib license.  You should have received a

 copy of the license along with this program; if not, please email

 <quantlib-dev@lists.sf.net>. The license is also available online at

 <http://quantlib.org/license.shtml>.

 This program is distributed in the hope that it will be useful, but WITHOUT

 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS

 FOR A PARTICULAR PURPOSE.  See the license for more details.

*/

#include <ql/math/statistics/generalstatistics.hpp>

namespace QuantLib {

    Real GeneralStatistics::weightSum() const {

        Real result = 0.0;

        std::vector<std::pair<Real,Real> >::const_iterator it;

        for (it=samples_.begin(); it!=samples_.end(); ++it) {

            result += it->second;

        }

        return result;

    }

    Real GeneralStatistics::mean() const {

        Size N = samples();

        QL_REQUIRE(N != 0, "empty sample set");

        return expectationValue([](Real x) { return x; }).first;

    }

    Real GeneralStatistics::variance() const {

        Size N = samples();

        QL_REQUIRE(N > 1,

                   "sample number <=1, unsufficient");

        // Subtract the mean and square. Repeat on the whole range.

        // Hopefully, the whole thing will be inlined in a single loop.

        Real m = mean();

        Real s2 = expectationValue([=](Real x) -> Real {

                      Real d = x - m;

                      return d * d;

                  }).first;

        return s2*N/(N-1.0);

    }

    Real GeneralStatistics::skewness() const {

        Size N = samples();

        QL_REQUIRE(N > 2,

                   "sample number <=2, unsufficient");

        Real m = mean();

        Real X = expectationValue([=](Real x) -> Real {

                     Real d = x - m;

                     return d * d * d;

                 }).first;

        Real sigma = standardDeviation();

        return (X/(sigma*sigma*sigma))*(N/(N-1.0))*(N/(N-2.0));

    }

    Real GeneralStatistics::kurtosis() const {

        Size N = samples();

        QL_REQUIRE(N > 3,

                   "sample number <=3, unsufficient");

        Real m = mean();

        Real X = expectationValue([=](Real x) -> Real {

                     Real d = x - m;

                     Real d2 = d * d;

                     return d2 * d2;

                 }).first;

        Real sigma2 = variance();

        Real c1 = (N/(N-1.0)) * (N/(N-2.0)) * ((N+1.0)/(N-3.0));

        Real c2 = 3.0 * ((N-1.0)/(N-2.0)) * ((N-1.0)/(N-3.0));

        return c1*(X/(sigma2*sigma2))-c2;

    }

    Real GeneralStatistics::percentile(Real percent) const {

        QL_REQUIRE(percent > 0.0 && percent <= 1.0,

                   "percentile (" << percent << ") must be in (0.0, 1.0]");

        Real sampleWeight = weightSum();

        QL_REQUIRE(sampleWeight>0.0,

                   "empty sample set");

        sort();

        std::vector<std::pair<Real,Real> >::iterator k, l;

        k = samples_.begin();

        l = samples_.end()-1;

        /* the sum of weight is non null, therefore there's

           at least one sample */

        Real integral = k->second, target = percent*sampleWeight;

        while (integral < target && k != l) {

            ++k;

            integral += k->second;

        }

        return k->first;

    }

    Real GeneralStatistics::topPercentile(Real percent) const {

        QL_REQUIRE(percent > 0.0 && percent <= 1.0,

                   "percentile (" << percent << ") must be in (0.0, 1.0]");

        Real sampleWeight = weightSum();

        QL_REQUIRE(sampleWeight > 0.0,

                   "empty sample set");

        sort();

        std::vector<std::pair<Real,Real> >::reverse_iterator k, l;

        k = samples_.rbegin();

        l = samples_.rend()-1;

        /* the sum of weight is non null, therefore there's

           at least one sample */

        Real integral = k->second, target = percent*sampleWeight;

        while (integral < target && k != l) {

            ++k;

            integral += k->second;

        }

        return k->first;

    }

}