Mercurial > hg > octave-lyh

annotate scripts/statistics/distributions/cauchy_inv.m @ 3426:f8dde1807dee

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
[project @ 2000-01-13 08:40:00 by jwe]
author jwe
date Thu, 13 Jan 2000 08:40:53 +0000
parents e4f4b2d26ee9
children 434790acb067
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
2 ##
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
3 ## This program is free software; you can redistribute it and/or modify
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
4 ## it under the terms of the GNU General Public License as published by
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
5 ## the Free Software Foundation; either version 2, or (at your option)
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
6 ## any later version.
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
7 ##
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
8 ## This program is distributed in the hope that it will be useful, but
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
9 ## WITHOUT ANY WARRANTY; without even the implied warranty of
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
11 ## General Public License for more details.
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
12 ##
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
13 ## You should have received a copy of the GNU General Public License
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
14 ## along with this file. If not, write to the Free Software Foundation,
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
16
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
17 ## usage: cauchy_inv (x [, lambda, sigma])
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
18 ##
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
19 ## For each element of x, compute the quantile (the inverse of the CDF)
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
20 ## at x of the Cauchy distribution with location parameter lambda and
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
21 ## scale parameter sigma. Default values are lambda = 0, sigma = 1.
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
22
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
23 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
24 ## Description: Quantile function of the Cauchy distribution
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
25
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
26 function inv = cauchy_inv (x, location, scale)
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
27
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
28 if !(nargin == 1 || nargin == 3)
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
29 usage ("cauchy_inv (x [, lambda, sigma])");
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
30 endif
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
31
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
32 if (nargin == 1)
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
33 location = 0;
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
34 scale = 1;
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
35 endif
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
36
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
37 [retval, x, location, scale] = common_size (x, location, scale);
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
38 if (retval > 0)
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
39 error (["cauchy_inv: ", ...
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
40 "x, lambda and sigma must be of common size or scalar"]);
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
41 endif
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
42
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
43 [r, c] = size (x);
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
44 s = r * c;
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
45 x = reshape (x, 1, s);
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
46 location = reshape (location, 1, s);
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
47 scale = reshape (scale, 1, s);
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
48
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
49 inv = NaN * ones (1, s);
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
50
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
51 ok = ((location > -Inf) & (location < Inf) &
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
52 (scale > 0) & (scale < Inf));
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
53
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
54 k = find ((x == 0) & ok);
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
55 if any (k)
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
56 inv(k) = -Inf * ones (1, length (k));
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
57 endif
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
58
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
59 k = find ((x > 0) & (x < 1) & ok);
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
60 if any (k)
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
61 inv(k) = location(k) - scale(k) .* cot (pi * x(k));
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
62 endif
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
63
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
64 k = find ((x == 1) & ok);
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
65 if any (k)
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
66 inv(k) = Inf * ones (1, length (k));
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
67 endif
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
68
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
69 inv = reshape (inv, r, c);
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3191
diff changeset
70
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
71 endfunction