octave-nkf: scripts/statistics/base/kurtosis.m annotate

annotate scripts/statistics/base/kurtosis.m @ 14399:d931d9b458fc

kurtosis.m: Make docstring equation prettier in Info format * kurtosis.m: Make docstring equation prettier in Info format

author	Rik <octave@nomad.inbox5.com>
date	Thu, 23 Feb 2012 20:07:25 -0800
parents	f3d52523cde1
children	f0e777cf348f

rev	line source
14138 72c96de7a403 maint: update copyright notices for 2012 John W. Eaton <jwe@octave.org> parents: 12656 diff changeset	1 ## Copyright (C) 1996-2012 John W. Eaton
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	2 ##
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	3 ## This file is part of Octave.
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	4 ##
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	6 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6754 diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6754 diff changeset	8 ## your option) any later version.
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	9 ##
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	10 ## 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	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	13 ## General Public License for more details.
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 ## 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	16 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6754 diff changeset	17 ## <http://www.gnu.org/licenses/>.
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	18
3367 0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	19 ## -- texinfo --
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	20 ## @deftypefn {Function File} {} kurtosis (@var{x})
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	21 ## @deftypefnx {Function File} {} kurtosis (@var{x}, @var{dim})
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	22 ## Compute the kurtosis of the elements of the vector @var{x}.
3367 0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	23 ## @tex
0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	24 ## $$
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	25 ## {\rm kurtosis} (x) = {1\over N \sigma^4} \sum_{i=1}^N (x_i-\bar{x})^4 - 3
3367 0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	26 ## $$
6754 451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe] jwe parents: 6046 diff changeset	27 ## where $\bar{x}$ is the mean value of $x$.
3367 0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	28 ## @end tex
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7411 diff changeset	29 ## @ifnottex
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3367 diff changeset	30 ##
3367 0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	31 ## @example
14399 d931d9b458fc kurtosis.m: Make docstring equation prettier in Info format Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	32 ## @group
d931d9b458fc kurtosis.m: Make docstring equation prettier in Info format Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	33 ## 1 sum ((x - mean(x)).^4)
d931d9b458fc kurtosis.m: Make docstring equation prettier in Info format Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	34 ## kurtosis (x) = --- * ---------------------- - 3
d931d9b458fc kurtosis.m: Make docstring equation prettier in Info format Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	35 ## N std(x)^4
d931d9b458fc kurtosis.m: Make docstring equation prettier in Info format Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	36 ## @end group
3367 0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	37 ## @end example
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10669 diff changeset	38 ##
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7411 diff changeset	39 ## @end ifnottex
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	40 ## If @var{x} is a matrix, return the kurtosis over the
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	41 ## first non-singleton dimension of the matrix. If the optional
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	42 ## @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	43 ##
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	44 ## Note: The definition of kurtosis above yields a kurtosis of zero for the
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	45 ## stdnormal distribution and is sometimes referred to as "excess kurtosis".
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	46 ## To calculate kurtosis without the normalization factor of @math{-3} use
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	47 ## @code{moment (@var{x}, 4, 'c') / std (@var{x})^4}.
12575 d0b799dafede Grammarcheck files for 3.4.1 release. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	48 ## @seealso{var, skewness, moment}
3367 0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	49 ## @end deftypefn
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	50
5428 2a16423e4aa0 [project @ 2005-08-23 18:38:27 by jwe] jwe parents: 5307 diff changeset	51 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	52 ## Created: 29 July 1994
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	53 ## Adapted-By: jwe
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	54
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	55 function retval = kurtosis (x, dim)
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	56
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	57 if (nargin != 1 && nargin != 2)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5428 diff changeset	58 print_usage ();
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	59 endif
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	60
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	61 if (! (isnumeric (x) \|\| islogical (x)))
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	62 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	63 endif
cab3b148d4e4 Improve validation of input arguments for base statistics functions. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	64
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	65 nd = ndims (x);
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	66 sz = size (x);
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	67 if (nargin != 2)
4886 54b076a24718 [project @ 2004-04-30 04:31:51 by jwe] jwe parents: 4885 diff changeset	68 ## Find the first non-singleton dimension.
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	69 (dim = find (sz > 1, 1)) \|\| (dim = 1);
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	70 else
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	71 if (!(isscalar (dim) && dim == fix (dim))
11149 fe3c3dfc07eb style fix: break lines before && and \|\|, not after John W. Eaton <jwe@octave.org> parents: 10821 diff changeset	72 \|\| !(1 <= dim && dim <= nd))
10669 cab3b148d4e4 Improve validation of input arguments for base statistics functions. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	73 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	74 endif
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	75 endif
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	76
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	77 n = sz(dim);
4886 54b076a24718 [project @ 2004-04-30 04:31:51 by jwe] jwe parents: 4885 diff changeset	78 sz(dim) = 1;
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	79 x = center (x, dim); # center also promotes integer to double for next line
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	80 retval = zeros (sz, class (x));
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	81 s = std (x, [], dim);
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	82 idx = find (s > 0);
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	83 x = sum (x.^4, dim);
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	84 retval(idx) = x(idx) ./ (n * s(idx) .^ 4) - 3;
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	85
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	86 endfunction
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	87
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	88
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	89 %!test
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	90 %! x = [-1; 0; 0; 0; 1];
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	91 %! y = [x, 2*x];
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	92 %! assert (kurtosis (y), [-1.4, -1.4], sqrt (eps));
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	93
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	94 %!assert (kurtosis (single (1)), single (0))
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	95
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	96 %% Test input validation
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	97 %!error kurtosis ()
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	98 %!error kurtosis (1, 2, 3)
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	99 %!error kurtosis (['A'; 'B'])
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	100 %!error kurtosis (1, ones (2,2))
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	101 %!error kurtosis (1, 1.5)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	102 %!error kurtosis (1, 0)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	103 %!error kurtosis (1, 3)
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	104

Mercurial > octave-nkf

annotate scripts/statistics/base/kurtosis.m @ 14399:d931d9b458fc