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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.
*/
/*! \file studenttdistribution.hpp
\brief Student's t-distribution
*/
#ifndef quantlib_student_t_distribution_hpp
#define quantlib_student_t_distribution_hpp
#include <ql/errors.hpp>
#include <ql/types.hpp>
#include <functional>
namespace QuantLib {
//! Student t-distribution
/*! Probability density function for \f$ n \f$ degrees of freedom
(see mathworld.wolfram.com or wikipedia.org):
\f[
f(x) = \frac {\Gamma\left(\frac{n+1}{2}\right)} {\sqrt{n\pi}
\, \Gamma\left(\frac{n}{2}\right)}\:
\frac {1} {\left(1+\frac{x^2}{n}\right)^{(n+1)/2}}
\f]
*/
class StudentDistribution {
public:
StudentDistribution(Integer n) : n_(n) {
QL_REQUIRE(n > 0, "invalid parameter for t-distribution");
}
Real operator()(Real x) const;
private:
Integer n_;
};
//! Cumulative Student t-distribution
/*! Cumulative distribution function for \f$ n \f$ degrees of freedom
(see mathworld.wolfram.com):
\f[
F(x) = \int_{-\infty}^x\,f(y)\,dy
= \frac{1}{2}\,
+\,\frac{1}{2}\,sgn(x)\,
\left[ I\left(1,\frac{n}{2},\frac{1}{2}\right)
- I\left(\frac{n}{n+y^2}, \frac{n}{2},\frac{1}{2}\right)\right]
\f]
where \f$ I(z; a, b) \f$ is the regularized incomplete beta function.
*/
class CumulativeStudentDistribution {
public:
CumulativeStudentDistribution(Integer n) : n_(n) {
QL_REQUIRE(n > 0, "invalid parameter for t-distribution");
}
Real operator()(Real x) const;
private:
Integer n_;
};
//! Inverse cumulative Student t-distribution
/*! \todo Find/implement an efficient algorithm for evaluating the
cumulative Student t-distribution, replacing the Newton
iteration
*/
class InverseCumulativeStudent {
public:
InverseCumulativeStudent(Integer n,
Real accuracy = 1e-6,
Size maxIterations = 50)
: d_(n), f_(n), accuracy_(accuracy),
maxIterations_(maxIterations) {}
Real operator()(Real x) const;
private:
StudentDistribution d_;
CumulativeStudentDistribution f_;
Real accuracy_;
Size maxIterations_;
};
}
#endif
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