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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;
}
}
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