generalstatistics.cpp

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/* -*- 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;
    }
 
}