Mercurial > octave-nkf
annotate scripts/statistics/distributions/tpdf.m @ 14138:72c96de7a403 stable
maint: update copyright notices for 2012
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Mon, 02 Jan 2012 14:25:41 -0500 |
parents | 583830ce6afa |
children | f3d52523cde1 |
rev | line source |
---|---|
14138
72c96de7a403
maint: update copyright notices for 2012
John W. Eaton <jwe@octave.org>
parents:
13181
diff
changeset
|
1 ## Copyright (C) 2012 Rik Wehbring |
72c96de7a403
maint: update copyright notices for 2012
John W. Eaton <jwe@octave.org>
parents:
13181
diff
changeset
|
2 ## Copyright (C) 1995-2012 Kurt Hornik |
5410 | 3 ## |
4 ## This file is part of Octave. | |
5 ## | |
6 ## Octave is free software; you can redistribute it and/or modify it | |
7 ## under the terms of the GNU General Public License as published by | |
7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
9 ## your option) any later version. | |
5410 | 10 ## |
11 ## Octave is distributed in the hope that it will be useful, but | |
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
14 ## General Public License for more details. | |
15 ## | |
16 ## You should have received a copy of the GNU General Public License | |
7016 | 17 ## along with Octave; see the file COPYING. If not, see |
18 ## <http://www.gnu.org/licenses/>. | |
5410 | 19 |
20 ## -*- texinfo -*- | |
5411 | 21 ## @deftypefn {Function File} {} tpdf (@var{x}, @var{n}) |
5410 | 22 ## For each element of @var{x}, compute the probability density function |
23 ## (PDF) at @var{x} of the @var{t} (Student) distribution with @var{n} | |
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
24 ## degrees of freedom. |
5410 | 25 ## @end deftypefn |
26 | |
5428 | 27 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
5410 | 28 ## Description: PDF of the t distribution |
29 | |
5411 | 30 function pdf = tpdf (x, n) |
5410 | 31 |
32 if (nargin != 2) | |
6046 | 33 print_usage (); |
5410 | 34 endif |
35 | |
36 if (!isscalar (n)) | |
37 [retval, x, n] = common_size (x, n); | |
38 if (retval > 0) | |
13171
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
39 error ("tpdf: X and N must be of common size or scalars"); |
5410 | 40 endif |
41 endif | |
42 | |
13171
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
43 if (iscomplex (x) || iscomplex (n)) |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
44 error ("tpdf: X and N must not be complex"); |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
45 endif |
5410 | 46 |
13171
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
47 if (isa (x, "single") || isa (n, "single")) |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
48 pdf = zeros (size (x), "single"); |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
49 else |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
50 pdf = zeros (size (x)); |
5410 | 51 endif |
52 | |
13171
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
53 k = isnan (x) | !(n > 0) | !(n < Inf); |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
54 pdf(k) = NaN; |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
55 |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
56 k = !isinf (x) & !isnan (x) & (n > 0) & (n < Inf); |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
57 if (isscalar (n)) |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
58 pdf(k) = (exp (- (n + 1) * log (1 + x(k) .^ 2 / n)/2) |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
59 / (sqrt (n) * beta (n/2, 1/2))); |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
60 else |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
61 pdf(k) = (exp (- (n(k) + 1) .* log (1 + x(k) .^ 2 ./ n(k))/2) |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
62 ./ (sqrt (n(k)) .* beta (n(k)/2, 1/2))); |
5410 | 63 endif |
64 | |
65 endfunction | |
13171
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
66 |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
67 |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
68 %!test |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
69 %! x = rand (10,1); |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
70 %! y = 1./(pi * (1 + x.^2)); |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
71 %! assert(tpdf (x, 1), y, 5*eps); |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
72 |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
73 %!shared x,y |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
74 %! x = [-Inf 0 0.5 1 Inf]; |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
75 %! y = 1./(pi * (1 + x.^2)); |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
76 %!assert(tpdf (x, ones(1,5)), y, eps); |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
77 %!assert(tpdf (x, 1), y, eps); |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
78 %!assert(tpdf (x, [0 NaN 1 1 1]), [NaN NaN y(3:5)], eps); |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
79 |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
80 %% Test class of input preserved |
13181
583830ce6afa
tpdf.m: Add eps to assert tests for passage on Mac OS
Rik <octave@nomad.inbox5.com>
parents:
13171
diff
changeset
|
81 %!assert(tpdf ([x, NaN], 1), [y, NaN], eps); |
13171
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
82 %!assert(tpdf (single([x, NaN]), 1), single([y, NaN]), eps("single")); |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
83 %!assert(tpdf ([x, NaN], single(1)), single([y, NaN]), eps("single")); |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
84 |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
85 %% Test input validation |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
86 %!error tpdf () |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
87 %!error tpdf (1) |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
88 %!error tpdf (1,2,3) |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
89 %!error tpdf (ones(3),ones(2)) |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
90 %!error tpdf (ones(2),ones(3)) |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
91 %!error tpdf (i, 2) |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
92 %!error tpdf (2, i) |
19b9f17d22af
Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
93 |