chdtr.c
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1 /* chdtr.c
2  *
3  * Chi-square distribution
4  *
5  *
6  *
7  * SYNOPSIS:
8  *
9  * double df, x, y, chdtr();
10  *
11  * y = chdtr( df, x );
12  *
13  *
14  *
15  * DESCRIPTION:
16  *
17  * Returns the area under the left hand tail (from 0 to x)
18  * of the Chi square probability density function with
19  * v degrees of freedom.
20  *
21  *
22  * inf.
23  * -
24  * 1 | | v/2-1 -t/2
25  * P( x | v ) = ----------- | t e dt
26  * v/2 - | |
27  * 2 | (v/2) -
28  * x
29  *
30  * where x is the Chi-square variable.
31  *
32  * The incomplete Gamma integral is used, according to the
33  * formula
34  *
35  * y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
36  *
37  *
38  * The arguments must both be positive.
39  *
40  *
41  *
42  * ACCURACY:
43  *
44  * See igam().
45  *
46  * ERROR MESSAGES:
47  *
48  * message condition value returned
49  * chdtr domain x < 0 or v < 1 0.0
50  */
51  /* chdtrc()
52  *
53  * Complemented Chi-square distribution
54  *
55  *
56  *
57  * SYNOPSIS:
58  *
59  * double v, x, y, chdtrc();
60  *
61  * y = chdtrc( v, x );
62  *
63  *
64  *
65  * DESCRIPTION:
66  *
67  * Returns the area under the right hand tail (from x to
68  * infinity) of the Chi square probability density function
69  * with v degrees of freedom:
70  *
71  *
72  * inf.
73  * -
74  * 1 | | v/2-1 -t/2
75  * P( x | v ) = ----------- | t e dt
76  * v/2 - | |
77  * 2 | (v/2) -
78  * x
79  *
80  * where x is the Chi-square variable.
81  *
82  * The incomplete Gamma integral is used, according to the
83  * formula
84  *
85  * y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
86  *
87  *
88  * The arguments must both be positive.
89  *
90  *
91  *
92  * ACCURACY:
93  *
94  * See igamc().
95  *
96  * ERROR MESSAGES:
97  *
98  * message condition value returned
99  * chdtrc domain x < 0 or v < 1 0.0
100  */
101  /* chdtri()
102  *
103  * Inverse of complemented Chi-square distribution
104  *
105  *
106  *
107  * SYNOPSIS:
108  *
109  * double df, x, y, chdtri();
110  *
111  * x = chdtri( df, y );
112  *
113  *
114  *
115  *
116  * DESCRIPTION:
117  *
118  * Finds the Chi-square argument x such that the integral
119  * from x to infinity of the Chi-square density is equal
120  * to the given cumulative probability y.
121  *
122  * This is accomplished using the inverse Gamma integral
123  * function and the relation
124  *
125  * x/2 = igamci( df/2, y );
126  *
127  *
128  *
129  *
130  * ACCURACY:
131  *
132  * See igami.c.
133  *
134  * ERROR MESSAGES:
135  *
136  * message condition value returned
137  * chdtri domain y < 0 or y > 1 0.0
138  * v < 1
139  *
140  */
141 
142 /* chdtr() */
143 
144 
145 /*
146  * Cephes Math Library Release 2.0: April, 1987
147  * Copyright 1984, 1987 by Stephen L. Moshier
148  * Direct inquiries to 30 Frost Street, Cambridge, MA 02140
149  */
150 
151 #include "mconf.h"
152 
153 double chdtrc(double df, double x)
154 {
155 
156  if (x < 0.0)
157  return 1.0; /* modified by T. Oliphant */
158  return (igamc(df / 2.0, x / 2.0));
159 }
160 
161 
162 
163 double chdtr(double df, double x)
164 {
165 
166  if ((x < 0.0)) { /* || (df < 1.0) ) */
167  sf_error("chdtr", SF_ERROR_DOMAIN, NULL);
168  return (NAN);
169  }
170  return (igam(df / 2.0, x / 2.0));
171 }
172 
173 
174 
175 double chdtri(double df, double y)
176 {
177  double x;
178 
179  if ((y < 0.0) || (y > 1.0)) { /* || (df < 1.0) ) */
180  sf_error("chdtri", SF_ERROR_DOMAIN, NULL);
181  return (NAN);
182  }
183 
184  x = igamci(0.5 * df, y);
185  return (2.0 * x);
186 }
igamc
double igamc(double a, double x)
Definition: igam.c:169
chdtr
double chdtr(double df, double x)
Definition: chdtr.c:163
x
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Definition: gnuplot_common_settings.hh:12
igam
double igam(double a, double x)
Definition: igam.c:128
y
Scalar * y
Definition: level1_cplx_impl.h:124
chdtri
double chdtri(double df, double y)
Definition: chdtr.c:175
chdtrc
double chdtrc(double df, double x)
Definition: chdtr.c:153
mconf.h
sf_error
void sf_error(const char *func_name, sf_error_t code, const char *fmt,...)
Definition: sf_error.c:41
NULL
#define NULL
Definition: ccolamd.c:609
SF_ERROR_DOMAIN
@ SF_ERROR_DOMAIN
Definition: sf_error.h:16
igamci
double igamci(double a, double q)
Definition: igami.c:301


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autogenerated on Sat Nov 16 2024 04:01:58