1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
|
/*************************************************************************
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
Contributors:
* Sergey Bochkanov (ALGLIB project). Translation from C to
pseudocode.
See subroutines comments for additional copyrights.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer listed
in this license in the documentation and/or other materials
provided with the distribution.
- Neither the name of the copyright holders nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*************************************************************************/
//#include <stdafx.h>
#include "chisquaredistr.h"
/*************************************************************************
Chi-square distribution
Returns the area under the left hand tail (from 0 to x)
of the Chi square probability density function with
v degrees of freedom.
x
-
1 | | v/2-1 -t/2
P( x | v ) = ----------- | t e dt
v/2 - | |
2 | (v/2) -
0
where x is the Chi-square variable.
The incomplete gamma integral is used, according to the
formula
y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
The arguments must both be positive.
ACCURACY:
See incomplete gamma function
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
*************************************************************************/
double chisquaredistribution(double v, double x)
{
double result;
ap::ap_error::make_assertion(x>=0&&v>=1, "Domain error in ChiSquareDistribution");
result = incompletegamma(v/2.0, x/2.0);
return result;
}
/*************************************************************************
Complemented Chi-square distribution
Returns the area under the right hand tail (from x to
infinity) of the Chi square probability density function
with v degrees of freedom:
inf.
-
1 | | v/2-1 -t/2
P( x | v ) = ----------- | t e dt
v/2 - | |
2 | (v/2) -
x
where x is the Chi-square variable.
The incomplete gamma integral is used, according to the
formula
y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
The arguments must both be positive.
ACCURACY:
See incomplete gamma function
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
*************************************************************************/
double chisquarecdistribution(double v, double x)
{
double result;
ap::ap_error::make_assertion(x>=0&&v>=1, "Domain error in ChiSquareDistributionC");
result = incompletegammac(v/2.0, x/2.0);
return result;
}
/*************************************************************************
Inverse of complemented Chi-square distribution
Finds the Chi-square argument x such that the integral
from x to infinity of the Chi-square density is equal
to the given cumulative probability y.
This is accomplished using the inverse gamma integral
function and the relation
x/2 = igami( df/2, y );
ACCURACY:
See inverse incomplete gamma function
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
*************************************************************************/
double invchisquaredistribution(double v, double y)
{
double result;
ap::ap_error::make_assertion(y>=0&&y<=1&&v>=1, "Domain error in InvChiSquareDistribution");
result = 2*invincompletegammac(0.5*v, y);
return result;
}
|
