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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 Roland Lichters
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
<https://www.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/distributions/studenttdistribution.hpp>
#include <ql/math/distributions/gammadistribution.hpp>
#include <ql/math/beta.hpp>
namespace QuantLib {
Real StudentDistribution::operator()(Real x) const {
static GammaFunction G;
Real g1 = std::exp (G.logValue(0.5 * (n_ + 1)));
Real g2 = std::exp (G.logValue(0.5 * n_));
Real power = std::pow (1. + x*x / n_, 0.5 * (n_ + 1));
return g1 / (g2 * power * std::sqrt (M_PI * n_));
}
Real CumulativeStudentDistribution::operator()(Real x) const {
Real xx = 1.0 * n_ / (x*x + n_);
Real sig = (x > 0 ? 1.0 : - 1.0);
return 0.5 + 0.5 * sig * ( incompleteBetaFunction (0.5 * n_, 0.5, 1.0)
-incompleteBetaFunction (0.5 * n_, 0.5, xx));
}
Real InverseCumulativeStudent::operator()(Real y) const {
QL_REQUIRE (y >= 0 && y <= 1, "argument out of range [0, 1]");
Real x = 0;
Size count = 0;
// do a few newton steps to find x
do {
x -= (f_(x) - y) / d_(x);
count++;
}
while (std::fabs(f_(x) - y) > accuracy_ && count < maxIterations_);
QL_REQUIRE (count < maxIterations_,
"maximum number of iterations " << maxIterations_
<< " reached in InverseCumulativeStudent, "
<< "y=" << y << ", x=" << x);
return x;
}
}
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