1 // inverse_chi_squared_distribution_find_df_example.cpp
2
3 // Copyright Paul A. Bristow 2010.
4 // Copyright Thomas Mang 2010.
5
6 // Use, modification and distribution are subject to the
7 // Boost Software License, Version 1.0.
8 // (See accompanying file LICENSE_1_0.txt
9 // or copy at http://www.boost.org/LICENSE_1_0.txt)
10
11 //#define BOOST_MATH_INSTRUMENT
12
13 // Example 1 of using inverse chi squared distribution
14 #include <boost/math/distributions/inverse_chi_squared.hpp>
15 using boost::math::inverse_chi_squared_distribution; // inverse_chi_squared_distribution.
16 using boost::math::inverse_chi_squared; //typedef for nverse_chi_squared_distribution double.
17
18 #include <iostream>
19 using std::cout; using std::endl;
20 #include <iomanip>
21 using std::setprecision;
22 using std::setw;
23 #include <cmath>
24 using std::sqrt;
25
main()26 int main()
27 {
28 cout << "Example using Inverse chi squared distribution to find df. " << endl;
29 try
30 {
31 cout.precision(std::numeric_limits<double>::max_digits10); //
32 int i = std::numeric_limits<double>::max_digits10;
33 cout << "Show all potentially significant decimal digits std::numeric_limits<double>::max_digits10 = " << i << endl;
34
35 cout.precision(3);
36 double nu = 10.;
37 double scale1 = 1./ nu; // 1st definition sigma^2 = 1/df;
38 double scale2 = 1.; // 2nd definition sigma^2 = 1
39 inverse_chi_squared sichsq(nu, 1/nu); // Explicitly scaled to default scale = 1/df.
40 inverse_chi_squared ichsq(nu); // Implicitly scaled to default scale = 1/df.
41 // Try degrees of freedom estimator
42
43 //double df = chi_squared::find_degrees_of_freedom(-diff, alpha[i], alpha[i], variance);
44
45 cout << "ichsq.degrees_of_freedom() = " << ichsq.degrees_of_freedom() << endl;
46
47 double diff = 0.5; // difference from variance to detect (delta).
48 double variance = 1.; // true variance
49 double alpha = 0.9;
50 double beta = 0.9;
51
52 cout << "diff = " << diff
53 << ", variance = " << variance << ", ratio = " << diff/variance
54 << ", alpha = " << alpha << ", beta = " << beta << endl;
55 using boost::math::detail::inverse_chi_square_df_estimator;
56 using boost::math::policies::default_policy;
57 inverse_chi_square_df_estimator<> a_df(alpha, beta, variance, diff);
58
59 cout << "df est" << endl;
60 for (double df = 1; df < 3; df += 0.1)
61 {
62 double est_df = a_df(1);
63 cout << df << " " << a_df(df) << endl;
64 }
65
66 //template <class F, class T, class Tol, class Policy>std::pair<T, T>
67 // bracket_and_solve_root(F f, const T& guess, T factor, bool rising, Tol tol, boost::uintmax_t& max_iter, const Policy& pol)
68
69
70 //double df = inverse_chi_squared_distribution<>::find_degrees_of_freedom(diff, alpha, beta, variance, 0);
71
72 double df = inverse_chi_squared::find_degrees_of_freedom(diff, alpha, beta, variance, 100);
73
74 cout << df << endl;
75 }
76 catch(const std::exception& e)
77 { // Always useful to include try & catch blocks because default policies
78 // are to throw exceptions on arguments that cause errors like underflow, overflow.
79 // Lacking try & catch blocks, the program will abort without a message below,
80 // which may give some helpful clues as to the cause of the exception.
81 std::cout <<
82 "\n""Message from thrown exception was:\n " << e.what() << std::endl;
83 }
84 return 0;
85 } // int main()
86
87 /*
88
89 Output is:
90
91 Example using Inverse chi squared distribution to find df.
92 Show all potentially significant decimal digits std::numeric_limits<double>::max_digits10 = 17
93 10
94
95 Message from thrown exception was:
96 Error in function boost::math::inverse_chi_squared_distribution<double>::inverse_chi_squared_distribution: Degrees of freedom argument is 1.#INF, but must be > 0 !
97 diff = 0.5, variance = 1, ratio = 0.5, alpha = 0.1, beta = 0.1
98 df est
99 1 1
100 ratio+1 = 1.5, quantile(0.1) = 0.00618, cdf = 6.5e-037, result = -0.1
101 1.1 -0.1
102 ratio+1 = 1.5, quantile(0.1) = 0.00903, cdf = 1.2e-025, result = -0.1
103 1.2 -0.1
104 ratio+1 = 1.5, quantile(0.1) = 0.0125, cdf = 8.25e-019, result = -0.1
105 1.3 -0.1
106 ratio+1 = 1.5, quantile(0.1) = 0.0166, cdf = 2.17e-014, result = -0.1
107 1.4 -0.1
108 ratio+1 = 1.5, quantile(0.1) = 0.0212, cdf = 2.2e-011, result = -0.1
109 1.5 -0.1
110 ratio+1 = 1.5, quantile(0.1) = 0.0265, cdf = 3e-009, result = -0.1
111 1.6 -0.1
112 ratio+1 = 1.5, quantile(0.1) = 0.0323, cdf = 1.11e-007, result = -0.1
113 1.7 -0.1
114 ratio+1 = 1.5, quantile(0.1) = 0.0386, cdf = 1.7e-006, result = -0.1
115 1.8 -0.1
116 ratio+1 = 1.5, quantile(0.1) = 0.0454, cdf = 1.41e-005, result = -0.1
117 1.9 -0.1
118 ratio+1 = 1.5, quantile(0.1) = 0.0527, cdf = 7.55e-005, result = -0.1
119 2 -0.1
120 ratio+1 = 1.5, quantile(0.1) = 0.0604, cdf = 0.000291, result = -0.1
121 2.1 -0.1
122 ratio+1 = 1.5, quantile(0.1) = 0.0685, cdf = 0.00088, result = -0.1
123 2.2 -0.1
124 ratio+1 = 1.5, quantile(0.1) = 0.0771, cdf = 0.0022, result = -0.0999
125 2.3 -0.0999
126 ratio+1 = 1.5, quantile(0.1) = 0.0859, cdf = 0.00475, result = -0.0997
127 2.4 -0.0997
128 ratio+1 = 1.5, quantile(0.1) = 0.0952, cdf = 0.00911, result = -0.0993
129 2.5 -0.0993
130 ratio+1 = 1.5, quantile(0.1) = 0.105, cdf = 0.0159, result = -0.0984
131 2.6 -0.0984
132 ratio+1 = 1.5, quantile(0.1) = 0.115, cdf = 0.0257, result = -0.0967
133 2.7 -0.0967
134 ratio+1 = 1.5, quantile(0.1) = 0.125, cdf = 0.039, result = -0.094
135 2.8 -0.094
136 ratio+1 = 1.5, quantile(0.1) = 0.135, cdf = 0.056, result = -0.0897
137 2.9 -0.0897
138 ratio+1 = 1.5, quantile(0.1) = 20.6, cdf = 1, result = 0.9
139
140 ichsq.degrees_of_freedom() = 10
141 diff = 0.5, variance = 1, ratio = 0.5, alpha = 0.9, beta = 0.9
142 df est
143 1 1
144 ratio+1 = 1.5, quantile(0.9) = 0.729, cdf = 0.269, result = -0.729
145 1.1 -0.729
146 ratio+1 = 1.5, quantile(0.9) = 0.78, cdf = 0.314, result = -0.693
147 1.2 -0.693
148 ratio+1 = 1.5, quantile(0.9) = 0.83, cdf = 0.36, result = -0.655
149 1.3 -0.655
150 ratio+1 = 1.5, quantile(0.9) = 0.879, cdf = 0.405, result = -0.615
151 1.4 -0.615
152 ratio+1 = 1.5, quantile(0.9) = 0.926, cdf = 0.449, result = -0.575
153 1.5 -0.575
154 ratio+1 = 1.5, quantile(0.9) = 0.973, cdf = 0.492, result = -0.535
155 1.6 -0.535
156 ratio+1 = 1.5, quantile(0.9) = 1.02, cdf = 0.534, result = -0.495
157 1.7 -0.495
158 ratio+1 = 1.5, quantile(0.9) = 1.06, cdf = 0.574, result = -0.455
159 1.8 -0.455
160 ratio+1 = 1.5, quantile(0.9) = 1.11, cdf = 0.612, result = -0.417
161 1.9 -0.417
162 ratio+1 = 1.5, quantile(0.9) = 1.15, cdf = 0.648, result = -0.379
163 2 -0.379
164 ratio+1 = 1.5, quantile(0.9) = 1.19, cdf = 0.681, result = -0.342
165 2.1 -0.342
166 ratio+1 = 1.5, quantile(0.9) = 1.24, cdf = 0.713, result = -0.307
167 2.2 -0.307
168 ratio+1 = 1.5, quantile(0.9) = 1.28, cdf = 0.742, result = -0.274
169 2.3 -0.274
170 ratio+1 = 1.5, quantile(0.9) = 1.32, cdf = 0.769, result = -0.242
171 2.4 -0.242
172 ratio+1 = 1.5, quantile(0.9) = 1.36, cdf = 0.793, result = -0.212
173 2.5 -0.212
174 ratio+1 = 1.5, quantile(0.9) = 1.4, cdf = 0.816, result = -0.184
175 2.6 -0.184
176 ratio+1 = 1.5, quantile(0.9) = 1.44, cdf = 0.836, result = -0.157
177 2.7 -0.157
178 ratio+1 = 1.5, quantile(0.9) = 1.48, cdf = 0.855, result = -0.133
179 2.8 -0.133
180 ratio+1 = 1.5, quantile(0.9) = 1.52, cdf = 0.872, result = -0.11
181 2.9 -0.11
182 ratio+1 = 1.5, quantile(0.9) = 29.6, cdf = 1, result = 0.1
183
184
185 */
186
187