1/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
2
3/*
4 Copyright (C) 2008 Roland Lichters
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/*! \file studenttdistribution.hpp
21 \brief Student's t-distribution
22*/
23
24#ifndef quantlib_student_t_distribution_hpp
25#define quantlib_student_t_distribution_hpp
26
27#include <ql/errors.hpp>
28#include <ql/types.hpp>
29#include <functional>
30
31namespace QuantLib {
32
33 //! Student t-distribution
34 /*! Probability density function for \f$ n \f$ degrees of freedom
35 (see mathworld.wolfram.com or wikipedia.org):
36 \f[
37 f(x) = \frac {\Gamma\left(\frac{n+1}{2}\right)} {\sqrt{n\pi}
38 \, \Gamma\left(\frac{n}{2}\right)}\:
39 \frac {1} {\left(1+\frac{x^2}{n}\right)^{(n+1)/2}}
40 \f]
41 */
42 class StudentDistribution {
43 public:
44 /*! \deprecated Use `auto` or `decltype` instead.
45 Deprecated in version 1.29.
46 */
47 QL_DEPRECATED
48 typedef Real argument_type;
49
50 /*! \deprecated Use `auto` or `decltype` instead.
51 Deprecated in version 1.29.
52 */
53 QL_DEPRECATED
54 typedef Real result_type;
55
56 StudentDistribution(Integer n) : n_(n) {
57 QL_REQUIRE(n > 0, "invalid parameter for t-distribution");
58 }
59 Real operator()(Real x) const;
60 private:
61 Integer n_;
62 };
63
64 //! Cumulative Student t-distribution
65 /*! Cumulative distribution function for \f$ n \f$ degrees of freedom
66 (see mathworld.wolfram.com):
67 \f[
68 F(x) = \int_{-\infty}^x\,f(y)\,dy
69 = \frac{1}{2}\,
70 +\,\frac{1}{2}\,sgn(x)\,
71 \left[ I\left(1,\frac{n}{2},\frac{1}{2}\right)
72 - I\left(\frac{n}{n+y^2}, \frac{n}{2},\frac{1}{2}\right)\right]
73 \f]
74 where \f$ I(z; a, b) \f$ is the regularized incomplete beta function.
75 */
76 class CumulativeStudentDistribution {
77 public:
78 /*! \deprecated Use `auto` or `decltype` instead.
79 Deprecated in version 1.29.
80 */
81 QL_DEPRECATED
82 typedef Real argument_type;
83
84 /*! \deprecated Use `auto` or `decltype` instead.
85 Deprecated in version 1.29.
86 */
87 QL_DEPRECATED
88 typedef Real result_type;
89
90 CumulativeStudentDistribution(Integer n) : n_(n) {
91 QL_REQUIRE(n > 0, "invalid parameter for t-distribution");
92 }
93 Real operator()(Real x) const;
94 private:
95 Integer n_;
96 };
97
98 //! Inverse cumulative Student t-distribution
99 /*! \todo Find/implement an efficient algorithm for evaluating the
100 cumulative Student t-distribution, replacing the Newton
101 iteration
102 */
103 class InverseCumulativeStudent {
104 public:
105 /*! \deprecated Use `auto` or `decltype` instead.
106 Deprecated in version 1.29.
107 */
108 QL_DEPRECATED
109 typedef Real argument_type;
110
111 /*! \deprecated Use `auto` or `decltype` instead.
112 Deprecated in version 1.29.
113 */
114 QL_DEPRECATED
115 typedef Real result_type;
116
117 InverseCumulativeStudent(Integer n,
118 Real accuracy = 1e-6,
119 Size maxIterations = 50)
120 : d_(n), f_(n), accuracy_(accuracy),
121 maxIterations_(maxIterations) {}
122 Real operator()(Real x) const;
123 private:
124 StudentDistribution d_;
125 CumulativeStudentDistribution f_;
126 Real accuracy_;
127 Size maxIterations_;
128 };
129
130}
131
132#endif
133

source code of quantlib/ql/math/distributions/studenttdistribution.hpp