-
Notifications
You must be signed in to change notification settings - Fork 57
/
toms179.html
279 lines (242 loc) · 7.17 KB
/
toms179.html
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
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
<html>
<head>
<title>
TOMS179 - Modified Beta Function
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TOMS179 <br> Modified Beta Function
</h1>
<hr>
<p>
<b>TOMS179</b>
is a MATLAB library which
implements ACM TOMS algorithm 179, for evaluating the modified
Beta function.
</p>
<p>
While the text of many ACM TOMS algorithms is available online
through ACM:
<a href = "http://www.acm.org/pubs/calgo/">
http://www.acm.org/pubs/calgo</a>
or NETLIB:
<a href = "http://www.netlib.org/toms/index.html">
http://www.netlib.org/toms/index.html</a>, many of the early
algorithms are not available. This is one of them. I typed it
in.
</p>
<p>
The original algorithm was published in the Algol language.
Shortly therafter, a distinct FORTRAN77 algorithm was published
as a "remark" to the original algorithm. A few modifications to
the FORTRAN77 program were proposed in a subsequent "remark".
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
[ <i>prob</i>, <i>ier</i> ] = <b>mdbeta</b> ( <i>x</i>, <i>p</i>, <i>q</i> )
</blockquote>
where
<ul>
<li>
<i>x</i> is the point of evaluation;
</li>
<li>
<i>p</i> and <i>q</i> are parameters;
</li>
<li>
<i>prob</i>, (output), is the computed probability;
</li>
<li>
<i>ier</i>, (output), is an error flag.
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TOMS179</b> is available in
<a href = "../../c_src/toms179/toms179.html">a C version</a> and
<a href = "../../cpp_src/toms179/toms179.html">a C++ version</a> and
<a href = "../../f77_src/toms179/toms179.html">a FORTRAN77 version</a> and
<a href = "../../f_src/toms179/toms179.html">a FORTRAN90 version</a> and
<a href = "../../m_src/toms179/toms179.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/asa063/asa063.html">
ASA063</a>,
a MATLAB library which
evaluates the incomplete Beta function.
</p>
<p>
<a href = "../../m_src/asa109/asa109.html">
ASA109</a>,
a MATLAB library which
inverts the incomplete Beta function.
</p>
<p>
<a href = "../../m_src/asa226/asa226.html">
ASA226</a>,
a MATLAB library which
evaluates the CDF of the noncentral Beta distribution.
</p>
<p>
<a href = "../../m_src/asa310/asa310.html">
ASA310</a>,
a MATLAB library which
computes the CDF of the noncentral Beta distribution.
</p>
<p>
<a href = "../../m_src/beta_nc/beta_nc.html">
BETA_NC</a>,
a MATLAB library which
evaluates the CDF of the noncentral Beta distribution.
</p>
<p>
<a href = "../../f_src/dcdflib/dcdflib.html">
DCDFLIB</a>,
a FORTRAN90 library which
contains routines which evaluate a number of probability density
functions, including one based on the Beta function.
</p>
<p>
<a href = "../../m_src/prob/prob.html">
PROB</a>,
a MATLAB library which
contains routines which evaluate a number of probability density
functions, including one based on the Beta function.
</p>
<p>
<a href = "../../m_src/test_values/test_values.html">
TEST_VALUES</a>,
a MATLAB library which
contains routines which return sample values of various functions,
including the modified beta function, and the logarithm of the
gamma function.
</p>
<p>
<a href = "../../f_src/toms708/toms708.html">
TOMS708</a>,
a FORTRAN90 library which
evaluates the incomplete beta function.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Nancy Bosten, EL Battiste,<br>
Remark on Algorithm 179:
Incomplete Beta Ratio,<br>
Communications of the ACM,<br>
Volume 17, Number 3, March 1974, pages 156-157.
</li>
<li>
William Cody, Kenneth Hillstrom,<br>
Chebyshev Approximations for the Natural Logarithm of the
Gamma Function,<br>
Mathematics of Computation,<br>
Volume 21, Number 98, April 1967, pages 198-203.
</li>
<li>
John Hart, Ward Cheney, Charles Lawson, Hans Maehly,
Charles Mesztenyi, John Rice, Henry Thacher,
Christoph Witzgall,<br>
Computer Approximations,<br>
Wiley, 1968,<br>
LC: QA297.C64.
</li>
<li>
Oliver Ludwig,<br>
Algorithm 179:
Incomplete Beta Ratio,<br>
Communications of the ACM,<br>
Volume 6, Number 6, June 1963, page 314.
</li>
<li>
Malcolm Pike, Jennie SooHoo,<br>
Remark on Algorithm 179:
Incomplete Beta Ratio,<br>
ACM Transactions on Mathematical Software,<br>
Volume 2, Number 2, June 1976, pages 207-208.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "alogam.m">alogam.m</a>
calculates the natural logarithm of GAMMA ( X ).
</li>
<li>
<a href = "beta_cdf_values.m">beta_cdf_values.m</a>
returns some values of the Beta CDF.
</li>
<li>
<a href = "gamma_log_values.m">gamma_log_values.m</a>
returns some values of the Log Gamma function.
</li>
<li>
<a href = "mdbeta.m">mdbeta.m</a>
evaluates the incomplete beta function.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>
<b>TIMESTAMP</b> prints out the current YMDHMS date as a timestamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "toms179_test.m">toms179_test.m</a>,
a sample calling program.
</li>
<li>
<a href = "toms179_test01.m">toms179_test01.m</a>,
tests ALOGAM.
</li>
<li>
<a href = "toms179_test02.m">toms179_test02.m</a>,
tests MDBETA.
</li>
<li>
<a href = "toms179_test_output.txt">toms179_test_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 30 January 2008.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>