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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2002, 2003 Sadruddin Rejeb
Copyright (C) 2007 Klaus Spanderen
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/solvers1d/brent.hpp>
#include <ql/math/functional.hpp>
#include <ql/math/distributions/chisquaredistribution.hpp>
#include <ql/math/distributions/gammadistribution.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
namespace QuantLib {
Real CumulativeChiSquareDistribution::operator()(Real x) const {
return CumulativeGammaDistribution(0.5*df_)(0.5*x);
}
Real NonCentralCumulativeChiSquareDistribution::operator()(Real x) const {
if (x <= 0.0)
return 0.0;
const Real errmax = 1e-12;
const Size itrmax = 10000;
Real lam = 0.5*ncp_;
Real u = std::exp(-lam);
Real v = u;
Real x2 = 0.5*x;
Real f2 = 0.5*df_;
Real f_x_2n = df_ - x;
Real t = 0.0;
if (f2*QL_EPSILON > 0.125 &&
std::fabs(x2-f2) < std::sqrt(QL_EPSILON)*f2) {
t = std::exp((1 - t) *
(2 - t/(f2+1)))/std::sqrt(2.0*M_PI*(f2 + 1.0));
}
else {
t = std::exp(f2*std::log(x2) - x2 -
GammaFunction().logValue(f2 + 1));
}
Real ans = v*t;
bool flag = false;
Size n = 1;
Real f_2n = df_ + 2.0;
f_x_2n += 2.0;
Real bound;
for (;;) {
if (f_x_2n > 0) {
flag = true;
goto L10;
}
for (;;) {
u *= lam / n;
v += u;
t *= x / f_2n;
ans += v*t;
n++;
f_2n += 2.0;
f_x_2n += 2.0;
if (!flag && n <= itrmax)
break;
L10:
bound = t * x / f_x_2n;
if (bound <= errmax || n > itrmax)
goto L_End;
}
}
L_End:
if (bound > errmax) QL_FAIL("didn't converge");
return (ans);
}
Real NonCentralCumulativeChiSquareSankaranApprox::operator()(Real x) const {
const Real h = 1-2*(df_+ncp_)*(df_+3*ncp_)/(3*square<Real>()(df_+2*ncp_));
const Real p = (df_+2*ncp_)/square<Real>()(df_+ncp_);
const Real m = (h-1)*(1-3*h);
const Real u= (std::pow(x/(df_+ncp_), h) - (1 + h*p*(h-1-0.5*(2-h)*m*p)))/
(h*std::sqrt(2*p)*(1+0.5*m*p));
return CumulativeNormalDistribution()(u);
}
InverseNonCentralCumulativeChiSquareDistribution::
InverseNonCentralCumulativeChiSquareDistribution(Real df, Real ncp,
Size maxEvaluations,
Real accuracy)
: nonCentralDist_(df, ncp),
guess_(df+ncp),
maxEvaluations_(maxEvaluations),
accuracy_(accuracy) {
}
Real InverseNonCentralCumulativeChiSquareDistribution::operator()(Real x) const {
// first find the right side of the interval
Real upper = guess_;
Size evaluations = maxEvaluations_;
while (nonCentralDist_(upper) < x && evaluations > 0) {
upper*=2.0;
--evaluations;
}
// use a Brent solver for the rest
Brent solver;
solver.setMaxEvaluations(evaluations);
return solver.solve(compose(subtract<Real>(x),
nonCentralDist_),
accuracy_, 0.75*upper,
(evaluations == maxEvaluations_)? 0.0: 0.5*upper,
upper);
}
}
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