|
3191
|
1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
|
3426
|
2 ## |
|
3922
|
3 ## This file is part of Octave. |
|
|
4 ## |
|
|
5 ## Octave is free software; you can redistribute it and/or modify it |
|
|
6 ## under the terms of the GNU General Public License as published by |
|
3191
|
7 ## the Free Software Foundation; either version 2, or (at your option) |
|
|
8 ## any later version. |
|
3426
|
9 ## |
|
3922
|
10 ## Octave is distributed in the hope that it will be useful, but |
|
3191
|
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
|
|
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
|
3426
|
13 ## General Public License for more details. |
|
|
14 ## |
|
3191
|
15 ## You should have received a copy of the GNU General Public License |
|
3922
|
16 ## along with Octave; see the file COPYING. If not, write to the Free |
|
5307
|
17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
|
|
18 ## 02110-1301, USA. |
|
3191
|
19 |
|
3456
|
20 ## -*- texinfo -*- |
|
|
21 ## @deftypefn {Function File} {} cauchy_inv (@var{x}, @var{lambda}, @var{sigma}) |
|
|
22 ## For each element of @var{x}, compute the quantile (the inverse of the |
|
|
23 ## CDF) at @var{x} of the Cauchy distribution with location parameter |
|
|
24 ## @var{lambda} and scale parameter @var{sigma}. Default values are |
|
|
25 ## @var{lambda} = 0, @var{sigma} = 1. |
|
|
26 ## @end deftypefn |
|
3191
|
27 |
|
5428
|
28 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
|
3456
|
29 ## Description: Quantile function of the Cauchy distribution |
|
3191
|
30 |
|
|
31 function inv = cauchy_inv (x, location, scale) |
|
3426
|
32 |
|
3456
|
33 if (! (nargin == 1 || nargin == 3)) |
|
6046
|
34 print_usage (); |
|
3191
|
35 endif |
|
3426
|
36 |
|
3191
|
37 if (nargin == 1) |
|
|
38 location = 0; |
|
|
39 scale = 1; |
|
|
40 endif |
|
3426
|
41 |
|
4854
|
42 if (!isscalar (location) || !isscalar (scale)) |
|
|
43 [retval, x, location, scale] = common_size (x, location, scale); |
|
|
44 if (retval > 0) |
|
|
45 error ("cauchy_inv: x, lambda and sigma must be of common size or scalar"); |
|
|
46 endif |
|
3191
|
47 endif |
|
3426
|
48 |
|
4854
|
49 sz = size (x); |
|
|
50 inv = NaN * ones (sz); |
|
3426
|
51 |
|
3191
|
52 ok = ((location > -Inf) & (location < Inf) & |
|
|
53 (scale > 0) & (scale < Inf)); |
|
3426
|
54 |
|
3191
|
55 k = find ((x == 0) & ok); |
|
3456
|
56 if (any (k)) |
|
4854
|
57 inv(k) = -Inf; |
|
3191
|
58 endif |
|
3426
|
59 |
|
3191
|
60 k = find ((x > 0) & (x < 1) & ok); |
|
3456
|
61 if (any (k)) |
|
4854
|
62 if (isscalar (location) && isscalar (scale)) |
|
|
63 inv(k) = location - scale .* cot (pi * x(k)); |
|
|
64 else |
|
|
65 inv(k) = location(k) - scale(k) .* cot (pi * x(k)); |
|
|
66 endif |
|
3191
|
67 endif |
|
3426
|
68 |
|
3191
|
69 k = find ((x == 1) & ok); |
|
3456
|
70 if (any (k)) |
|
4854
|
71 inv(k) = Inf; |
|
3191
|
72 endif |
|
3426
|
73 |
|
3191
|
74 endfunction |
