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

annotate scripts/statistics/base/quantile.m @ 10549:95c3e38098bf

Untabify .m scripts

author	Rik <code@nomad.inbox5.com>
date	Fri, 23 Apr 2010 11:28:50 -0700
parents	9f25290a35e8
children	be55736a0783

rev	line source
9899 9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	1 ## Copyright (C) 2008, 2009 Ben Abbott and Jaroslav Hajek
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	2 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	3 ## This file is part of Octave.
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	4 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	6 ## under the terms of the GNU General Public License as published by
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	8 ## your option) any later version.
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	9 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	13 ## General Public License for more details.
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	14 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	15 ## You should have received a copy of the GNU General Public License
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	16 ## along with Octave; see the file COPYING. If not, see
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	17 ## <http://www.gnu.org/licenses/>.
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	18
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	19 ## -- texinfo --
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	20 ## @deftypefn {Function File} {@var{q} =} quantile (@var{x}, @var{p})
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	21 ## @deftypefnx {Function File} {@var{q} =} quantile (@var{x}, @var{p}, @var{dim})
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8506 diff changeset	22 ## @deftypefnx {Function File} {@var{q} =} quantile (@var{x}, @var{p}, @var{dim}, @var{method})
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	23 ## For a sample, @var{x}, calculate the quantiles, @var{q}, corresponding to
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	24 ## the cumulative probability values in @var{p}. All non-numeric values (NaNs) of
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	25 ## @var{x} are ignored.
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	26 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	27 ## If @var{x} is a matrix, compute the quantiles for each column and
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	28 ## return them in a matrix, such that the i-th row of @var{q} contains
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	29 ## the @var{p}(i)th quantiles of each column of @var{x}.
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	30 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	31 ## The optional argument @var{dim} determines the dimension along which
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	32 ## the percentiles are calculated. If @var{dim} is omitted, and @var{x} is
1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	33 ## a vector or matrix, it defaults to 1 (column wise quantiles). In the
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	34 ## instance that @var{x} is a N-d array, @var{dim} defaults to the first
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	35 ## dimension whose size greater than unity.
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	36 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	37 ## The methods available to calculate sample quantiles are the nine methods
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	38 ## used by R (http://www.r-project.org/). The default value is METHOD = 5.
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	39 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	40 ## Discontinuous sample quantile methods 1, 2, and 3
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	41 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	42 ## @enumerate 1
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	43 ## @item Method 1: Inverse of empirical distribution function.
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	44 ## @item Method 2: Similar to method 1 but with averaging at discontinuities.
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	45 ## @item Method 3: SAS definition: nearest even order statistic.
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	46 ## @end enumerate
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	47 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	48 ## Continuous sample quantile methods 4 through 9, where p(k) is the linear
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	49 ## interpolation function respecting each methods' representative cdf.
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	50 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	51 ## @enumerate 4
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	52 ## @item Method 4: p(k) = k / n. That is, linear interpolation of the empirical cdf.
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	53 ## @item Method 5: p(k) = (k - 0.5) / n. That is a piecewise linear function where
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	54 ## the knots are the values midway through the steps of the empirical cdf.
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	55 ## @item Method 6: p(k) = k / (n + 1).
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	56 ## @item Method 7: p(k) = (k - 1) / (n - 1).
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	57 ## @item Method 8: p(k) = (k - 1/3) / (n + 1/3). The resulting quantile estimates
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	58 ## are approximately median-unbiased regardless of the distribution of @var{x}.
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	59 ## @item Method 9: p(k) = (k - 3/8) / (n + 1/4). The resulting quantile estimates
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	60 ## are approximately unbiased for the expected order statistics if @var{x} is
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	61 ## normally distributed.
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	62 ## @end enumerate
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	63 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	64 ## Hyndman and Fan (1996) recommend method 8. Maxima, S, and R
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	65 ## (versions prior to 2.0.0) use 7 as their default. Minitab and SPSS
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	66 ## use method 6. @sc{matlab} uses method 5.
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	67 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	68 ## References:
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	69 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	70 ## @itemize @bullet
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	71 ## @item Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New
9069 634274aaa183 Cleanup documentation for stats.texi Rik <rdrider0-list@yahoo.com> parents: 9051 diff changeset	72 ## S Language. Wadsworth & Brooks/Cole.
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	73 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	74 ## @item Hyndman, R. J. and Fan, Y. (1996) Sample quantiles in
9069 634274aaa183 Cleanup documentation for stats.texi Rik <rdrider0-list@yahoo.com> parents: 9051 diff changeset	75 ## statistical packages, American Statistician, 50, 361--365.
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	76 ##
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	77 ## @item R: A Language and Environment for Statistical Computing;
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	78 ## @url{http://cran.r-project.org/doc/manuals/fullrefman.pdf}.
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	79 ## @end itemize
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	80 ## @end deftypefn
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	81
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	82 ## Author: Ben Abbott <bpabbott@mac.com>
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	83 ## Description: Matlab style quantile function of a discrete/continuous distribution
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	84
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	85 function q = quantile (x, p, dim, method)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	86
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	87 if (nargin < 1 \|\| nargin > 4)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	88 print_usage ();
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	89 endif
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	90
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	91 if (nargin < 2)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	92 p = [0.00 0.25, 0.50, 0.75, 1.00];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	93 endif
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	94
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	95 if (nargin < 3)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	96 dim = 1;
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	97 endif
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	98
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	99 if (nargin < 4)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	100 method = 5;
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	101 endif
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	102
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	103 if (dim > ndims(x))
8664 e07e93c04080 style fixes John W. Eaton <jwe@octave.org> parents: 8507 diff changeset	104 error ("quantile: invalid dimension");
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	105 endif
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	106
8506 bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7643 diff changeset	107 ## Set the permutation vector.
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	108 perm = 1:ndims(x);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	109 perm(1) = dim;
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	110 perm(dim) = 1;
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	111
8506 bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7643 diff changeset	112 ## Permute dim to the 1st index.
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	113 x = permute (x, perm);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	114
8506 bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7643 diff changeset	115 ## Save the size of the permuted x N-d array.
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	116 sx = size (x);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	117
8506 bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7643 diff changeset	118 ## Reshape to a 2-d array.
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	119 x = reshape (x, [sx(1), prod(sx(2:end))]);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	120
8506 bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7643 diff changeset	121 ## Calculate the quantiles.
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	122 q = __quantile__ (x, p, method);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	123
8506 bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7643 diff changeset	124 ## Return the shape to the original N-d array.
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	125 q = reshape (q, [numel(p), sx(2:end)]);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	126
8506 bc982528de11 comment style fixes John W. Eaton <jwe@octave.org> parents: 7643 diff changeset	127 ## Permute the 1st index back to dim.
7643 0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	128 q = ipermute (q, perm);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	129
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	130 endfunction
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	131
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	132 %!test
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	133 %! p = 0.5;
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	134 %! x = sort (rand (11));
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	135 %! q = quantile (x, p);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	136 %! assert (q, x(6,:))
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	137 %! x = x.';
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	138 %! q = quantile (x, p, 2);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	139 %! assert (q, x(:,6));
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	140
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	141 %!test
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	142 %! p = [0.00, 0.25, 0.50, 0.75, 1.00];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	143 %! x = [1; 2; 3; 4];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	144 %! a = [1.0000 1.0000 2.0000 3.0000 4.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	145 %! 1.0000 1.5000 2.5000 3.5000 4.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	146 %! 1.0000 1.0000 2.0000 3.0000 4.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	147 %! 1.0000 1.0000 2.0000 3.0000 4.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	148 %! 1.0000 1.5000 2.5000 3.5000 4.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	149 %! 1.0000 1.2500 2.5000 3.7500 4.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	150 %! 1.0000 1.7500 2.5000 3.2500 4.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	151 %! 1.0000 1.4167 2.5000 3.5833 4.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	152 %! 1.0000 1.4375 2.5000 3.5625 4.0000];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	153 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	154 %! q = quantile (x, p, 1, m).';
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	155 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	156 %! endfor
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	157
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	158 %!test
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	159 %! p = [0.00, 0.25, 0.50, 0.75, 1.00];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	160 %! x = [1; 2; 3; 4; 5];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	161 %! a = [1.0000 2.0000 3.0000 4.0000 5.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	162 %! 1.0000 2.0000 3.0000 4.0000 5.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	163 %! 1.0000 1.0000 2.0000 4.0000 5.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	164 %! 1.0000 1.2500 2.5000 3.7500 5.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	165 %! 1.0000 1.7500 3.0000 4.2500 5.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	166 %! 1.0000 1.5000 3.0000 4.5000 5.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	167 %! 1.0000 2.0000 3.0000 4.0000 5.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	168 %! 1.0000 1.6667 3.0000 4.3333 5.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	169 %! 1.0000 1.6875 3.0000 4.3125 5.0000];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	170 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	171 %! q = quantile (x, p, 1, m).';
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	172 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	173 %! endfor
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	174
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	175 %!test
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	176 %! p = [0.00, 0.25, 0.50, 0.75, 1.00];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	177 %! x = [1; 2; 5; 9];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	178 %! a = [1.0000 1.0000 2.0000 5.0000 9.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	179 %! 1.0000 1.5000 3.5000 7.0000 9.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	180 %! 1.0000 1.0000 2.0000 5.0000 9.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	181 %! 1.0000 1.0000 2.0000 5.0000 9.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	182 %! 1.0000 1.5000 3.5000 7.0000 9.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	183 %! 1.0000 1.2500 3.5000 8.0000 9.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	184 %! 1.0000 1.7500 3.5000 6.0000 9.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	185 %! 1.0000 1.4167 3.5000 7.3333 9.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	186 %! 1.0000 1.4375 3.5000 7.2500 9.0000];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	187 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	188 %! q = quantile (x, p, 1, m).';
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	189 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	190 %! endfor
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	191
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	192 %!test
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	193 %! p = [0.00, 0.25, 0.50, 0.75, 1.00];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	194 %! x = [1; 2; 5; 9; 11];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	195 %! a = [1.0000 2.0000 5.0000 9.0000 11.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	196 %! 1.0000 2.0000 5.0000 9.0000 11.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	197 %! 1.0000 1.0000 2.0000 9.0000 11.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	198 %! 1.0000 1.2500 3.5000 8.0000 11.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	199 %! 1.0000 1.7500 5.0000 9.5000 11.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	200 %! 1.0000 1.5000 5.0000 10.0000 11.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	201 %! 1.0000 2.0000 5.0000 9.0000 11.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	202 %! 1.0000 1.6667 5.0000 9.6667 11.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	203 %! 1.0000 1.6875 5.0000 9.6250 11.0000];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	204 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	205 %! q = quantile (x, p, 1, m).';
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	206 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	207 %! endfor
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	208
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	209 %!test
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	210 %! p = [0.00, 0.25, 0.50, 0.75, 1.00];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	211 %! x = [16; 11; 15; 12; 15; 8; 11; 12; 6; 10];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	212 %! a = [6.0000 10.0000 11.0000 15.0000 16.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	213 %! 6.0000 10.0000 11.5000 15.0000 16.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	214 %! 6.0000 8.0000 11.0000 15.0000 16.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	215 %! 6.0000 9.0000 11.0000 13.5000 16.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	216 %! 6.0000 10.0000 11.5000 15.0000 16.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	217 %! 6.0000 9.5000 11.5000 15.0000 16.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	218 %! 6.0000 10.2500 11.5000 14.2500 16.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	219 %! 6.0000 9.8333 11.5000 15.0000 16.0000
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	220 %! 6.0000 9.8750 11.5000 15.0000 16.0000];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	221 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	222 %! q = quantile (x, p, 1, m).';
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	223 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	224 %! endfor
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	225
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	226 %!test
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	227 %! p = [0.00, 0.25, 0.50, 0.75, 1.00];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	228 %! x = [-0.58851; 0.40048; 0.49527; -2.551500; -0.52057; ...
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	229 %! -0.17841; 0.057322; -0.62523; 0.042906; 0.12337];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	230 %! a = [-2.551474 -0.588505 -0.178409 0.123366 0.495271
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	231 %! -2.551474 -0.588505 -0.067751 0.123366 0.495271
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	232 %! -2.551474 -0.625231 -0.178409 0.123366 0.495271
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	233 %! -2.551474 -0.606868 -0.178409 0.090344 0.495271
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	234 %! -2.551474 -0.588505 -0.067751 0.123366 0.495271
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	235 %! -2.551474 -0.597687 -0.067751 0.192645 0.495271
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	236 %! -2.551474 -0.571522 -0.067751 0.106855 0.495271
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	237 %! -2.551474 -0.591566 -0.067751 0.146459 0.495271
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	238 %! -2.551474 -0.590801 -0.067751 0.140686 0.495271];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	239 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	240 %! q = quantile (x, p, 1, m).';
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	241 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	242 %! endfor
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	243
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	244 %!test
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	245 %! p = 0.5;
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	246 %! x = [0.112600, 0.114800, 0.052100, 0.236400, 0.139300
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	247 %! 0.171800, 0.727300, 0.204100, 0.453100, 0.158500
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	248 %! 0.279500, 0.797800, 0.329600, 0.556700, 0.730700
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	249 %! 0.428800, 0.875300, 0.647700, 0.628700, 0.816500
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	250 %! 0.933100, 0.931200, 0.963500, 0.779600, 0.846100];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	251 %! tol = 0.00001;
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	252 %! x(5,5) = NaN;
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	253 %! assert (quantile(x, p, 1), [0.27950, 0.79780, 0.32960, 0.55670, 0.44460], tol);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	254 %! x(1,1) = NaN;
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	255 %! assert (quantile(x, p, 1), [0.35415, 0.79780, 0.32960, 0.55670, 0.44460], tol);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	256 %! x(3,3) = NaN;
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	257 %! assert (quantile(x, p, 1), [0.35415, 0.79780, 0.42590, 0.55670, 0.44460], tol);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	258
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	259 %!test
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	260 %! sx = [2, 3, 4];
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	261 %! x = rand (sx);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	262 %! dim = 2;
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	263 %! p = 0.5;
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	264 %! yobs = quantile (x, p, dim);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	265 %! yexp = median (x, dim);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	266 %! assert (yobs, yexp);
0220da981c2a Modified statistics to calculate consistent median. Ben Abbott <bpabbott@mac.com> parents: diff changeset	267
9899 9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	268 ## For the cumulative probability values in @var{p}, compute the
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	269 ## quantiles, @var{q} (the inverse of the cdf), for the sample, @var{x}.
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	270 ##
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	271 ## The optional input, @var{method}, refers to nine methods available in R
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	272 ## (http://www.r-project.org/). The default is @var{method} = 7. For more
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	273 ## detail, see `help quantile'.
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	274 ## @seealso{prctile, quantile, statistics}
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	275
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	276 ## Author: Ben Abbott <bpabbott@mac.com>
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	277 ## Vectorized version: Jaroslav Hajek <highegg@gmail.com>
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	278 ## Description: Quantile function of a empirical samples
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	279
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	280 function inv = __quantile__ (x, p, method = 5)
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	281
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	282 if (nargin < 2 \|\| nargin > 3)
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	283 print_usage ();
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	284 endif
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	285
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	286 if (! ismatrix (x))
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	287 error ("quantile: x must be a matrix");
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	288 endif
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	289
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	290 ## Save length and set shape of quantiles.
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	291 n = numel (p);
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	292 p = p(:);
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	293
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	294 ## Save length and set shape of samples.
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	295 ## FIXME: does sort guarantee that NaN's come at the end?
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	296 x = sort (x);
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	297 m = sum (! isnan (x));
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	298 mx = size (x, 1);
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	299 nx = size (x, 2);
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	300
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	301 ## Initialize output values.
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	302 inv = Inf*(-(p < 0) + (p > 1));
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	303 inv = repmat (inv, 1, nx);
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	304
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	305 ## Do the work.
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	306 if (any(k = find((p >= 0) & (p <= 1))))
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	307 n = length (k);
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	308 p = p (k);
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	309 ## Special case.
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	310 if (mx == 1)
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	311 inv(k,:) = repmat (x, n, 1);
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	312 return
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	313 endif
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	314
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	315 ## The column-distribution indices.
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	316 pcd = kron (ones (n, 1), mx*(0:nx-1));
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	317 mm = kron (ones (n, 1), m);
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	318 switch method
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	319 case {1, 2, 3}
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	320 switch method
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	321 case 1
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	322 p = max (ceil (kron (p, m)), 1);
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	323 inv(k,:) = x(p + pcd);
9899 9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	324
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	325 case 2
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	326 p = kron (p, m);
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	327 p_lr = max (ceil (p), 1);
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	328 p_rl = min (floor (p + 1), mm);
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	329 inv(k,:) = (x(p_lr + pcd) + x(p_rl + pcd))/2;
9899 9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	330
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	331 case 3
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	332 ## Used by SAS, method PCTLDEF=2.
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	333 ## http://support.sas.com/onlinedoc/913/getDoc/en/statug.hlp/stdize_sect14.htm
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	334 t = max (kron (p, m), 1);
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	335 t = roundb (t);
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	336 inv(k,:) = x(t + pcd);
9899 9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	337 endswitch
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	338
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	339 otherwise
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	340 switch method
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	341 case 4
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	342 p = kron (p, m);
9899 9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	343
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	344 case 5
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	345 ## Used by Matlab.
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	346 p = kron (p, m) + 0.5;
9899 9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	347
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	348 case 6
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	349 ## Used by Minitab and SPSS.
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	350 p = kron (p, m+1);
9899 9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	351
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	352 case 7
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	353 ## Used by S and R.
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	354 p = kron (p, m-1) + 1;
9899 9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	355
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	356 case 8
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	357 ## Median unbiased .
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	358 p = kron (p, m+1/3) + 1/3;
9899 9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	359
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	360 case 9
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	361 ## Approximately unbiased respecting order statistics.
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	362 p = kron (p, m+0.25) + 0.375;
9899 9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	363
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	364 otherwise
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	365 error ("quantile: Unknown method, '%d'", method);
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	366 endswitch
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	367
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	368 ## Duplicate single values.
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	369 imm1 = mm == 1;
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	370 x(2,imm1) = x(1,imm1);
9899 9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	371
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	372 ## Interval indices.
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	373 pi = max (min (floor (p), mm-1), 1);
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	374 pr = max (min (p - pi, 1), 0);
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	375 pi += pcd;
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9899 diff changeset	376 inv(k,:) = (1-pr) .* x(pi) + pr .* x(pi+1);
9899 9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	377 endswitch
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	378 endif
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	379
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9069 diff changeset	380 endfunction

Mercurial > octave-nkf

annotate scripts/statistics/base/quantile.m @ 10549:95c3e38098bf