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

annotate scripts/statistics/base/kurtosis.m @ 12575:d0b799dafede

Grammarcheck files for 3.4.1 release.

author	Rik <octave@nomad.inbox5.com>
date	Mon, 04 Apr 2011 15:33:46 -0700
parents	c792872f8942
children	6b2f14af2360

rev	line source
11523 fd0a3ac60b0e update copyright notices John W. Eaton <jwe@octave.org> parents: 11436 diff changeset	1 ## Copyright (C) 1996-2011 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
0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	32 ## kurtosis (x) = N^(-1) std(x)^(-4) sum ((x - mean(x)).^4) - 3
0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	33 ## @end example
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10669 diff changeset	34 ##
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7411 diff changeset	35 ## @end ifnottex
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	36 ## 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	37 ## 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	38 ## @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	39 ##
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	40 ## 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	41 ## 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	42 ## 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	43 ## @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	44 ## @seealso{var, skewness, moment}
3367 0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	45 ## @end deftypefn
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	46
5428 2a16423e4aa0 [project @ 2005-08-23 18:38:27 by jwe] jwe parents: 5307 diff changeset	47 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	48 ## Created: 29 July 1994
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	49 ## Adapted-By: jwe
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	50
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	51 function retval = kurtosis (x, dim)
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	52
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	53 if (nargin != 1 && nargin != 2)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5428 diff changeset	54 print_usage ();
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	55 endif
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	56
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	57 if (!isnumeric (x))
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	58 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	59 endif
cab3b148d4e4 Improve validation of input arguments for base statistics functions. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	60
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	61 nd = ndims (x);
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	62 sz = size (x);
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	63 if (nargin != 2)
4886 54b076a24718 [project @ 2004-04-30 04:31:51 by jwe] jwe parents: 4885 diff changeset	64 ## Find the first non-singleton dimension.
10669 cab3b148d4e4 Improve validation of input arguments for base statistics functions. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	65 dim = find (sz > 1, 1);
cab3b148d4e4 Improve validation of input arguments for base statistics functions. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	66 if (isempty (dim))
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	67 dim = 1;
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	68 endif
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	69 else
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	70 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	71 \|\| !(1 <= dim && dim <= nd))
10669 cab3b148d4e4 Improve validation of input arguments for base statistics functions. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	72 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	73 endif
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	74 endif
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	75
4886 54b076a24718 [project @ 2004-04-30 04:31:51 by jwe] jwe parents: 4885 diff changeset	76 c = sz(dim);
54b076a24718 [project @ 2004-04-30 04:31:51 by jwe] jwe parents: 4885 diff changeset	77 sz(dim) = 1;
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	78 idx = ones (1, nd);
4886 54b076a24718 [project @ 2004-04-30 04:31:51 by jwe] jwe parents: 4885 diff changeset	79 idx(dim) = c;
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	80 x = x - repmat (mean (x, dim), idx);
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	81 retval = zeros (sz, class (x));
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	82 s = std (x, [], dim);
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);
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	84 ind = find (s > 0);
4886 54b076a24718 [project @ 2004-04-30 04:31:51 by jwe] jwe parents: 4885 diff changeset	85 retval(ind) = x(ind) ./ (c * s(ind) .^ 4) - 3;
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	86
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	87 endfunction
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	88
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	89
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	90 %!test
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	91 %! x = [-1; 0; 0; 0; 1];
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	92 %! y = [x, 2*x];
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	93 %! assert(all (abs (kurtosis (y) - [-1.4, -1.4]) < sqrt (eps)));
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	94
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	95 %% Test input validation
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	96 %!error kurtosis ()
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	97 %!error kurtosis (1, 2, 3)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	98 %!error kurtosis (true(1,2))
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	99 %!error kurtosis (1, ones(2,2))
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	100 %!error kurtosis (1, 1.5)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	101 %!error kurtosis (1, 0)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11149 diff changeset	102 %!error kurtosis (1, 3)
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	103

Mercurial > octave-libtiff

annotate scripts/statistics/base/kurtosis.m @ 12575:d0b799dafede