Mercurial > octave

annotate scripts/statistics/kurtosis.m @ 31706:597f3ee61a48 stable

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
update Octave Project Developers copyright for the new year
author John W. Eaton <jwe@octave.org>
date Fri, 06 Jan 2023 13:11:27 -0500
parents 5d3faba0342e
children 2e484f9f1f18
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
27923
bd51beb6205e update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents: 27919
diff changeset
1 ########################################################################
bd51beb6205e update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents: 27919
diff changeset
2 ##
31706
597f3ee61a48 update Octave Project Developers copyright for the new year
John W. Eaton <jwe@octave.org>
parents: 30875
diff changeset
3 ## Copyright (C) 1996-2023 The Octave Project Developers
27918
b442ec6dda5c use centralized file for copyright info for individual contributors
John W. Eaton <jwe@octave.org>
parents: 26596
diff changeset
4 ##
27923
bd51beb6205e update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents: 27919
diff changeset
5 ## See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents: 27919
diff changeset
6 ## distribution or <https://octave.org/copyright/>.
3200
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
7 ##
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
8 ## This file is part of Octave.
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
9 ##
24534
194eb4bd202b maint: Update punctuation for GPL v3 license text.
Rik <rik@octave.org>
parents: 24512
diff changeset
10 ## Octave is free software: you can redistribute it and/or modify it
3200
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
11 ## under the terms of the GNU General Public License as published by
24534
194eb4bd202b maint: Update punctuation for GPL v3 license text.
Rik <rik@octave.org>
parents: 24512
diff changeset
12 ## the Free Software Foundation, either version 3 of the License, or
22755
3a2b891d0b33 maint: Standardize Copyright formatting.
Rik <rik@octave.org>
parents: 22323
diff changeset
13 ## (at your option) any later version.
3200
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
14 ##
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
15 ## Octave is distributed in the hope that it will be useful, but
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
22755
3a2b891d0b33 maint: Standardize Copyright formatting.
Rik <rik@octave.org>
parents: 22323
diff changeset
17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3a2b891d0b33 maint: Standardize Copyright formatting.
Rik <rik@octave.org>
parents: 22323
diff changeset
18 ## GNU General Public License for more details.
3200
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
19 ##
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
20 ## You should have received a copy of the GNU General Public License
7016
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 6754
diff changeset
21 ## along with Octave; see the file COPYING. If not, see
24534
194eb4bd202b maint: Update punctuation for GPL v3 license text.
Rik <rik@octave.org>
parents: 24512
diff changeset
22 ## <https://www.gnu.org/licenses/>.
27923
bd51beb6205e update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents: 27919
diff changeset
23 ##
bd51beb6205e update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents: 27919
diff changeset
24 ########################################################################
3200
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
25
3367
0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe]
jwe
parents: 3200
diff changeset
26 ## -*- texinfo -*-
30875
5d3faba0342e doc: Ensure documentation lists output argument when it exists for all m-files.
Rik <rik@octave.org>
parents: 30564
diff changeset
27 ## @deftypefn {} {@var{y} =} kurtosis (@var{x})
5d3faba0342e doc: Ensure documentation lists output argument when it exists for all m-files.
Rik <rik@octave.org>
parents: 30564
diff changeset
28 ## @deftypefnx {} {@var{y} =} kurtosis (@var{x}, @var{flag})
5d3faba0342e doc: Ensure documentation lists output argument when it exists for all m-files.
Rik <rik@octave.org>
parents: 30564
diff changeset
29 ## @deftypefnx {} {@var{y} =} kurtosis (@var{x}, @var{flag}, @var{dim})
20174
d9341b422488 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19833
diff changeset
30 ## Compute the sample kurtosis of the elements of @var{x}.
d9341b422488 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19833
diff changeset
31 ##
d9341b422488 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19833
diff changeset
32 ## The sample kurtosis is defined as
3367
0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe]
jwe
parents: 3200
diff changeset
33 ## @tex
0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe]
jwe
parents: 3200
diff changeset
34 ## $$
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
35 ## \kappa_1 = {{{1\over N}\,
24511
4f0e6ee6c9b8 Make documentation Sec 26.1 more consistent and Sec 25.4 clearer (bug #52685)
Daniel J Sebald <daniel.sebald@ieee.org>
parents: 23219
diff changeset
36 ## \sum_{i=1}^N (x_i - \bar{x})^4} \over \sigma^4},
3367
0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe]
jwe
parents: 3200
diff changeset
37 ## $$
24511
4f0e6ee6c9b8 Make documentation Sec 26.1 more consistent and Sec 25.4 clearer (bug #52685)
Daniel J Sebald <daniel.sebald@ieee.org>
parents: 23219
diff changeset
38 ## where $N$ is the length of @var{x}, $\bar{x}$ its mean, and $\sigma$
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
39 ## its (uncorrected) standard deviation.
3367
0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe]
jwe
parents: 3200
diff changeset
40 ## @end tex
8517
81d6ab3ac93c Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents: 7411
diff changeset
41 ## @ifnottex
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3367
diff changeset
42 ##
3367
0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe]
jwe
parents: 3200
diff changeset
43 ## @example
14399
d931d9b458fc kurtosis.m: Make docstring equation prettier in Info format
Rik <octave@nomad.inbox5.com>
parents: 14363
diff changeset
44 ## @group
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
45 ## mean ((@var{x} - mean (@var{x})).^4)
17698
9bb5d3f63cdd NEWS: Announce change in definition of kurtosis function for Matlab compatibility.
Rik <rik@octave.org>
parents: 17697
diff changeset
46 ## k1 = ------------------------
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
47 ## std (@var{x}).^4
14399
d931d9b458fc kurtosis.m: Make docstring equation prettier in Info format
Rik <octave@nomad.inbox5.com>
parents: 14363
diff changeset
48 ## @end group
3367
0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe]
jwe
parents: 3200
diff changeset
49 ## @end example
10821
693e22af08ae Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents: 10669
diff changeset
50 ##
8517
81d6ab3ac93c Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents: 7411
diff changeset
51 ## @end ifnottex
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
52 ##
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
53 ## @noindent
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
54 ## The optional argument @var{flag} controls which normalization is used.
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
55 ## If @var{flag} is equal to 1 (default value, used when @var{flag} is omitted
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
56 ## or empty), return the sample kurtosis as defined above. If @var{flag} is
17698
9bb5d3f63cdd NEWS: Announce change in definition of kurtosis function for Matlab compatibility.
Rik <rik@octave.org>
parents: 17697
diff changeset
57 ## equal to 0, return the @w{"bias-corrected"} kurtosis coefficient instead:
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
58 ## @tex
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
59 ## $$
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
60 ## \kappa_0 = 3 + {\scriptstyle N - 1 \over \scriptstyle (N - 2)(N - 3)} \,
17698
9bb5d3f63cdd NEWS: Announce change in definition of kurtosis function for Matlab compatibility.
Rik <rik@octave.org>
parents: 17697
diff changeset
61 ## \left( (N + 1)\, \kappa_1 - 3 (N - 1) \right)
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
62 ## $$
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
63 ## @end tex
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
64 ## @ifnottex
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
65 ##
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
66 ## @example
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
67 ## @group
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
68 ## N - 1
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
69 ## k0 = 3 + -------------- * ((N + 1) * k1 - 3 * (N - 1))
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
70 ## (N - 2)(N - 3)
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
71 ## @end group
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
72 ## @end example
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
73 ##
24985
d85b2485af9e doc: grammarcheck m-files ahead of 4.4 release.
Rik <rik@octave.org>
parents: 24547
diff changeset
74 ## @noindent
24511
4f0e6ee6c9b8 Make documentation Sec 26.1 more consistent and Sec 25.4 clearer (bug #52685)
Daniel J Sebald <daniel.sebald@ieee.org>
parents: 23219
diff changeset
75 ## where @math{N} is the length of the @var{x} vector.
4f0e6ee6c9b8 Make documentation Sec 26.1 more consistent and Sec 25.4 clearer (bug #52685)
Daniel J Sebald <daniel.sebald@ieee.org>
parents: 23219
diff changeset
76 ##
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
77 ## @end ifnottex
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
78 ## The bias-corrected kurtosis coefficient is obtained by replacing the sample
17698
9bb5d3f63cdd NEWS: Announce change in definition of kurtosis function for Matlab compatibility.
Rik <rik@octave.org>
parents: 17697
diff changeset
79 ## second and fourth central moments by their unbiased versions. It is an
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
80 ## unbiased estimate of the population kurtosis for normal populations.
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
81 ##
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
82 ## If @var{x} is a matrix, or more generally a multi-dimensional array, return
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
83 ## the kurtosis along the first non-singleton dimension. If the optional
11436
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11149
diff changeset
84 ## @var{dim} argument is given, operate along this dimension.
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
85 ##
12575
d0b799dafede Grammarcheck files for 3.4.1 release.
Rik <octave@nomad.inbox5.com>
parents: 11587
diff changeset
86 ## @seealso{var, skewness, moment}
3367
0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe]
jwe
parents: 3200
diff changeset
87 ## @end deftypefn
3200
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
88
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
89 function y = kurtosis (x, flag, dim)
3200
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
90
28789
28de41192f3c Eliminate unneeded verification of nargin, nargout in m-files.
Rik <rik@octave.org>
parents: 27985
diff changeset
91 if (nargin < 1)
6046
34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe]
jwe
parents: 5428
diff changeset
92 print_usage ();
3200
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
93 endif
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
94
12656
6b2f14af2360 Overhaul functions in statistics/base directory.
Rik <octave@nomad.inbox5.com>
parents: 12575
diff changeset
95 if (! (isnumeric (x) || islogical (x)))
11436
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11149
diff changeset
96 error ("kurtosis: X must be a numeric vector or matrix");
10669
cab3b148d4e4 Improve validation of input arguments for base statistics functions.
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
97 endif
cab3b148d4e4 Improve validation of input arguments for base statistics functions.
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
98
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
99 if (nargin < 2 || isempty (flag))
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
100 flag = 1; # default: do not use the "bias corrected" version
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
101 else
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
102 if (! isscalar (flag) || (flag != 0 && flag != 1))
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
103 error ("kurtosis: FLAG must be 0 or 1");
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
104 endif
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
105 endif
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
106
4885
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe]
jwe
parents: 4030
diff changeset
107 nd = ndims (x);
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe]
jwe
parents: 4030
diff changeset
108 sz = size (x);
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
109 if (nargin < 3)
4886
54b076a24718 [project @ 2004-04-30 04:31:51 by jwe]
jwe
parents: 4885
diff changeset
110 ## Find the first non-singleton dimension.
12656
6b2f14af2360 Overhaul functions in statistics/base directory.
Rik <octave@nomad.inbox5.com>
parents: 12575
diff changeset
111 (dim = find (sz > 1, 1)) || (dim = 1);
3200
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
112 else
21309
7fbecef105ca Allow statistics functions to work over non-existent dimension (bug #33523).
Rik <rik@octave.org>
parents: 21308
diff changeset
113 if (! (isscalar (dim) && dim == fix (dim) && dim > 0))
10669
cab3b148d4e4 Improve validation of input arguments for base statistics functions.
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
114 error ("kurtosis: DIM must be an integer and a valid dimension");
4885
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe]
jwe
parents: 4030
diff changeset
115 endif
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe]
jwe
parents: 4030
diff changeset
116 endif
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
117
21309
7fbecef105ca Allow statistics functions to work over non-existent dimension (bug #33523).
Rik <rik@octave.org>
parents: 21308
diff changeset
118 n = size (x, dim);
4886
54b076a24718 [project @ 2004-04-30 04:31:51 by jwe]
jwe
parents: 4885
diff changeset
119 sz(dim) = 1;
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
120
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
121 x = center (x, dim); # center also promotes integer, logical to double
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
122 v = var (x, 1, dim); # normalize with 1/N
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
123 y = sum (x .^ 4, dim);
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
124 idx = (v != 0);
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
125 y(idx) = y(idx) ./ (n * v(idx) .^ 2);
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
126 y(! idx) = NaN;
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
127
19593
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 17744
diff changeset
128 ## Apply bias correction to the second and fourth central sample moment
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
129 if (flag == 0)
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
130 if (n > 3)
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
131 C = (n - 1) / ((n - 2) * (n - 3));
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
132 y = 3 + C * ((n + 1) * y - 3 * (n - 1));
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
133 else
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
134 y(:) = NaN;
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
135 endif
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
136 endif
4885
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe]
jwe
parents: 4030
diff changeset
137
3200
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
diff changeset
138 endfunction
7411
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe]
jwe
parents: 7017
diff changeset
139
11436
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11149
diff changeset
140
7411
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe]
jwe
parents: 7017
diff changeset
141 %!test
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe]
jwe
parents: 7017
diff changeset
142 %! x = [-1; 0; 0; 0; 1];
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe]
jwe
parents: 7017
diff changeset
143 %! y = [x, 2*x];
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
144 %! assert (kurtosis (y), [2.5, 2.5], sqrt (eps));
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
145
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
146 %!assert (kurtosis ([-3, 0, 1]) == kurtosis ([-1, 0, 3]))
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
147 %!assert (kurtosis (ones (3, 5)), NaN (1, 5))
21309
7fbecef105ca Allow statistics functions to work over non-existent dimension (bug #33523).
Rik <rik@octave.org>
parents: 21308
diff changeset
148 %!assert (kurtosis (1, [], 3), NaN)
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
149
30330
01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599)
Rik <rik@octave.org>
parents: 29359
diff changeset
150 %!assert (kurtosis ([1:5 10; 1:5 10], 0, 2),
01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599)
Rik <rik@octave.org>
parents: 29359
diff changeset
151 %! 5.4377317925288901 * [1; 1], 8 * eps)
01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599)
Rik <rik@octave.org>
parents: 29359
diff changeset
152 %!assert (kurtosis ([1:5 10; 1:5 10], 1, 2),
01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599)
Rik <rik@octave.org>
parents: 29359
diff changeset
153 %! 2.9786509002956195 * [1; 1], 8 * eps)
01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599)
Rik <rik@octave.org>
parents: 29359
diff changeset
154 %!assert (kurtosis ([1:5 10; 1:5 10], [], 2),
01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599)
Rik <rik@octave.org>
parents: 29359
diff changeset
155 %! 2.9786509002956195 * [1; 1], 8 * eps)
12656
6b2f14af2360 Overhaul functions in statistics/base directory.
Rik <octave@nomad.inbox5.com>
parents: 12575
diff changeset
156
21308
c53bfd6d8e08 maint: Use American spelling for "behavior".
Rik <rik@octave.org>
parents: 20852
diff changeset
157 ## Test behavior on single input
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
158 %!assert (kurtosis (single ([1:5 10])), single (2.9786513), eps ("single"))
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
159 %!assert (kurtosis (single ([1 2]), 0), single (NaN))
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
160
26596
cc0d942d0e20 Remove inconsistent warning "Octave:divide-by-zero" (bug #46650).
Kai T. Ohlhus <k.ohlhus@gmail.com>
parents: 26376
diff changeset
161 ## Verify no warnings
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
162 %!test
20515
76f67400649e Use '-local' option to warning to simplify BIST tests.
Rik <rik@octave.org>
parents: 20174
diff changeset
163 %! lastwarn (""); # clear last warning
76f67400649e Use '-local' option to warning to simplify BIST tests.
Rik <rik@octave.org>
parents: 20174
diff changeset
164 %! kurtosis (1);
76f67400649e Use '-local' option to warning to simplify BIST tests.
Rik <rik@octave.org>
parents: 20174
diff changeset
165 %! assert (lastwarn (), "");
7411
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe]
jwe
parents: 7017
diff changeset
166
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
167 ## Test input validation
28886
d8318c12d903 test: remove unnecessary BIST tests in m-files checking for excessive number of inputs.
Rik <rik@octave.org>
parents: 28789
diff changeset
168 %!error <Invalid call> kurtosis ()
17697
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
169 %!error <X must be a numeric vector or matrix> kurtosis (['A'; 'B'])
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
170 %!error <FLAG must be 0 or 1> kurtosis (1, 2)
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
171 %!error <FLAG must be 0 or 1> kurtosis (1, [1 0])
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
172 %!error <DIM must be an integer> kurtosis (1, [], ones (2,2))
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
173 %!error <DIM must be an integer> kurtosis (1, [], 1.5)
f0e777cf348f kurtosis.m: Improve compatibility with Matlab's kurtosis function
Julien Bect <julien.bect@supelec.fr>
parents: 14399
diff changeset
174 %!error <DIM must be .* a valid dimension> kurtosis (1, [], 0)