| 1 | /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ |
|---|---|
| 2 | |
| 3 | /* |
| 4 | Copyright (C) 2002, 2003 Sadruddin Rejeb |
| 5 | |
| 6 | This file is part of QuantLib, a free-software/open-source library |
| 7 | for financial quantitative analysts and developers - http://quantlib.org/ |
| 8 | |
| 9 | QuantLib is free software: you can redistribute it and/or modify it |
| 10 | under the terms of the QuantLib license. You should have received a |
| 11 | copy of the license along with this program; if not, please email |
| 12 | <quantlib-dev@lists.sf.net>. The license is also available online at |
| 13 | <http://quantlib.org/license.shtml>. |
| 14 | |
| 15 | This program is distributed in the hope that it will be useful, but WITHOUT |
| 16 | ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS |
| 17 | FOR A PARTICULAR PURPOSE. See the license for more details. |
| 18 | */ |
| 19 | |
| 20 | #include <ql/math/distributions/gammadistribution.hpp> |
| 21 | |
| 22 | namespace QuantLib { |
| 23 | |
| 24 | Real CumulativeGammaDistribution::operator()(Real x) const { |
| 25 | if (x <= 0.0) return 0.0; |
| 26 | |
| 27 | Real gln = GammaFunction().logValue(x: a_); |
| 28 | |
| 29 | if (x<(a_+1.0)) { |
| 30 | Real ap = a_; |
| 31 | Real del = 1.0/a_; |
| 32 | Real sum = del; |
| 33 | for (Size n=1; n<=100; n++) { |
| 34 | ap += 1.0; |
| 35 | del *= x/ap; |
| 36 | sum += del; |
| 37 | if (std::fabs(x: del) < std::fabs(x: sum)*3.0e-7) |
| 38 | return sum*std::exp(x: -x + a_*std::log(x: x) - gln); |
| 39 | } |
| 40 | } else { |
| 41 | Real b = x + 1.0 - a_; |
| 42 | Real c = QL_MAX_REAL; |
| 43 | Real d = 1.0/b; |
| 44 | Real h = d; |
| 45 | for (Size n=1; n<=100; n++) { |
| 46 | Real an = -1.0*n*(n-a_); |
| 47 | b += 2.0; |
| 48 | d = an*d + b; |
| 49 | if (std::fabs(x: d) < QL_EPSILON) d = QL_EPSILON; |
| 50 | c = b + an/c; |
| 51 | if (std::fabs(x: c) < QL_EPSILON) c = QL_EPSILON; |
| 52 | d = 1.0/d; |
| 53 | Real del = d*c; |
| 54 | h *= del; |
| 55 | if (std::fabs(x: del - 1.0)<QL_EPSILON) |
| 56 | return 1.0-h*std::exp(x: -x + a_*std::log(x: x) - gln); |
| 57 | } |
| 58 | } |
| 59 | QL_FAIL("too few iterations"); |
| 60 | } |
| 61 | |
| 62 | const Real GammaFunction::c1_ = 76.18009172947146; |
| 63 | const Real GammaFunction::c2_ = -86.50532032941677; |
| 64 | const Real GammaFunction::c3_ = 24.01409824083091; |
| 65 | const Real GammaFunction::c4_ = -1.231739572450155; |
| 66 | const Real GammaFunction::c5_ = 0.1208650973866179e-2; |
| 67 | const Real GammaFunction::c6_ = -0.5395239384953e-5; |
| 68 | |
| 69 | Real GammaFunction::logValue(Real x) const { |
| 70 | QL_REQUIRE(x>0.0, "positive argument required"); |
| 71 | Real temp = x + 5.5; |
| 72 | temp -= (x + 0.5)*std::log(x: temp); |
| 73 | Real ser=1.000000000190015; |
| 74 | ser += c1_/(x + 1.0); |
| 75 | ser += c2_/(x + 2.0); |
| 76 | ser += c3_/(x + 3.0); |
| 77 | ser += c4_/(x + 4.0); |
| 78 | ser += c5_/(x + 5.0); |
| 79 | ser += c6_/(x + 6.0); |
| 80 | |
| 81 | return -temp+std::log(x: 2.5066282746310005*ser/x); |
| 82 | } |
| 83 | |
| 84 | Real GammaFunction::value(Real x) const { |
| 85 | if (x >= 1.0) { |
| 86 | return std::exp(x: logValue(x)); |
| 87 | } |
| 88 | else { |
| 89 | if (x > -20.0) { |
| 90 | // \Gamma(x) = \frac{\Gamma(x+1)}{x} |
| 91 | return value(x: x+1.0)/x; |
| 92 | } |
| 93 | else { |
| 94 | // \Gamma(-x) = -\frac{\pi}{\Gamma(x)\sin(\pi x) x} |
| 95 | return -M_PI/(value(x: -x)*x*std::sin(M_PI*x)); |
| 96 | } |
| 97 | } |
| 98 | } |
| 99 | } |
| 100 |