/usr/include/ql/math/distributions/binomialdistribution.hpp is in libquantlib0-dev 1.7.1-1.
This file is owned by root:root, with mode 0o644.
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/*
Copyright (C) 2003 Ferdinando Ametrano
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.
*/
/*! \file binomialdistribution.hpp
\brief Binomial distribution
*/
#ifndef quantlib_binomial_distribution_h
#define quantlib_binomial_distribution_h
#include <ql/math/factorial.hpp>
#include <ql/math/beta.hpp>
namespace QuantLib {
inline Real binomialCoefficientLn(BigNatural n, BigNatural k) {
QL_REQUIRE(n>=k, "n<k not allowed");
return Factorial::ln(n)-Factorial::ln(k)-Factorial::ln(n-k);
}
inline Real binomialCoefficient(BigNatural n, BigNatural k) {
return std::floor(0.5+std::exp(binomialCoefficientLn(n, k)));
}
//! Binomial probability distribution function
/*! formula here ...
Given an integer k it returns its probability in a Binomial
distribution with parameters p and n.
*/
class BinomialDistribution : public std::unary_function<Real,Real> {
public:
BinomialDistribution(Real p, BigNatural n);
// function
Real operator()(BigNatural k) const;
private:
BigNatural n_;
Real logP_, logOneMinusP_;
};
//! Cumulative binomial distribution function
/*! Given an integer k it provides the cumulative probability
of observing kk<=k:
formula here ...
*/
class CumulativeBinomialDistribution
: public std::unary_function<Real,Real> {
public:
CumulativeBinomialDistribution(Real p, BigNatural n);
// function
Real operator()(BigNatural k) const {
if (k >= n_)
return 1.0;
else
return 1.0 - incompleteBetaFunction(k+1, n_-k, p_);
}
private:
BigNatural n_;
Real p_;
};
inline BinomialDistribution::BinomialDistribution(Real p,
BigNatural n)
: n_(n) {
if (p==0.0) {
logP_ = -QL_MAX_REAL;
logOneMinusP_ = 0.0;
} else if (p==1.0) {
logP_ = 0.0;
logOneMinusP_ = -QL_MAX_REAL;
} else {
QL_REQUIRE(p>0, "negative p not allowed");
QL_REQUIRE(p<1.0, "p>1.0 not allowed");
logP_ = std::log(p);
logOneMinusP_ = std::log(1.0-p);
}
}
inline
CumulativeBinomialDistribution::CumulativeBinomialDistribution(
Real p, BigNatural n)
: n_(n), p_(p) {
QL_REQUIRE(p>=0, "negative p not allowed");
QL_REQUIRE(p<=1.0, "p>1.0 not allowed");
}
inline Real BinomialDistribution::operator()(BigNatural k) const {
if (k > n_) return 0.0;
// p==1.0
if (logP_==0.0)
return (k==n_ ? 1.0 : 0.0);
// p==0.0
else if (logOneMinusP_==0.0)
return (k==0 ? 1.0 : 0.0);
else
return std::exp(binomialCoefficientLn(n_, k) +
k * logP_ + (n_-k) * logOneMinusP_);
}
/*! Given an odd integer n and a real number z it returns p such that:
1 - CumulativeBinomialDistribution((n-1)/2, n, p) =
CumulativeNormalDistribution(z)
\pre n must be odd
*/
inline Real PeizerPrattMethod2Inversion(Real z, BigNatural n) {
QL_REQUIRE(n%2==1,
"n must be an odd number: " << n << " not allowed");
Real result = (z/(n+1.0/3.0+0.1/(n+1.0)));
result *= result;
result = std::exp(-result*(n+1.0/6.0));
result = 0.5 + (z>0 ? 1 : -1) * std::sqrt((0.25 * (1.0-result)));
return result;
}
}
#endif
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