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Add quantile, prctile functions to documentation.
author Rik <octave@nomad.inbox5.com>
date Sat, 02 Apr 2011 13:37:52 -0700
parents 139f993936af
children 4e32a1bb9096 f96b9b9f141b
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1 ## Copyright (C) 2008-2011 Ben Abbott and Jaroslav Hajek
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {@var{q} =} quantile (@var{x}, @var{p})
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21 ## @deftypefnx {Function File} {@var{q} =} quantile (@var{x}, @var{p}, @var{dim})
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22 ## @deftypefnx {Function File} {@var{q} =} quantile (@var{x}, @var{p}, @var{dim}, @var{method})
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23 ## For a sample, @var{x}, calculate the quantiles, @var{q}, corresponding to
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24 ## the cumulative probability values in @var{p}. All non-numeric values (NaNs)
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25 ## of @var{x} are ignored.
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26 ##
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27 ## If @var{x} is a matrix, compute the quantiles for each column and
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28 ## return them in a matrix, such that the i-th row of @var{q} contains
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29 ## the @var{p}(i)th quantiles of each column of @var{x}.
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30 ##
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31 ## The optional argument @var{dim} determines the dimension along which
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32 ## the quantiles are calculated. If @var{dim} is omitted, and @var{x} is
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33 ## a vector or matrix, it defaults to 1 (column-wise quantiles). If
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34 ## @var{x} is an N-d array, @var{dim} defaults to the first non-singleton
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35 ## dimension.
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36 ##
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37 ## The methods available to calculate sample quantiles are the nine methods
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38 ## used by R (http://www.r-project.org/). The default value is METHOD = 5.
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39 ##
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40 ## Discontinuous sample quantile methods 1, 2, and 3
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41 ##
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42 ## @enumerate 1
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43 ## @item Method 1: Inverse of empirical distribution function.
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44 ##
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45 ## @item Method 2: Similar to method 1 but with averaging at discontinuities.
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46 ##
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47 ## @item Method 3: SAS definition: nearest even order statistic.
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48 ## @end enumerate
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49 ##
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50 ## Continuous sample quantile methods 4 through 9, where p(k) is the linear
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51 ## interpolation function respecting each methods' representative cdf.
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52 ##
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53 ## @enumerate 4
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54 ## @item Method 4: p(k) = k / n. That is, linear interpolation of the
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55 ## empirical cdf.
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56 ##
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57 ## @item Method 5: p(k) = (k - 0.5) / n. That is a piecewise linear function
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58 ## where the knots are the values midway through the steps of the empirical
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59 ## cdf.
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60 ##
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61 ## @item Method 6: p(k) = k / (n + 1).
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62 ##
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63 ## @item Method 7: p(k) = (k - 1) / (n - 1).
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64 ##
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65 ## @item Method 8: p(k) = (k - 1/3) / (n + 1/3). The resulting quantile
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66 ## estimates are approximately median-unbiased regardless of the distribution
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67 ## of @var{x}.
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68 ##
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69 ## @item Method 9: p(k) = (k - 3/8) / (n + 1/4). The resulting quantile
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70 ## estimates are approximately unbiased for the expected order statistics if
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71 ## @var{x} is normally distributed.
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72 ## @end enumerate
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73 ##
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74 ## Hyndman and Fan (1996) recommend method 8. Maxima, S, and R
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75 ## (versions prior to 2.0.0) use 7 as their default. Minitab and SPSS
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76 ## use method 6. @sc{matlab} uses method 5.
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77 ##
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78 ## References:
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79 ##
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80 ## @itemize @bullet
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81 ## @item Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New
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82 ## S Language. Wadsworth & Brooks/Cole.
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83 ##
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84 ## @item Hyndman, R. J. and Fan, Y. (1996) Sample quantiles in
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85 ## statistical packages, American Statistician, 50, 361--365.
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86 ##
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87 ## @item R: A Language and Environment for Statistical Computing;
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88 ## @url{http://cran.r-project.org/doc/manuals/fullrefman.pdf}.
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89 ## @end itemize
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90 ##
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91 ## Examples:
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92 ##
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93 ## @example
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94 ## @group
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95 ## x = randi (1000, [10, 1]); # Create random empirical data in range 1-1000
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96 ## q = quantile (x, [0, 1]); # Return minimum, maximum of empirical distribution
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97 ## q = quantile (x, [0.25 0.5 0.75]); # Return quartiles of empirical distribution
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98 ## @end group
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99 ## @end example
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100 ## @seealso{prctile}
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101 ## @end deftypefn
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102
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103 ## Author: Ben Abbott <bpabbott@mac.com>
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104 ## Description: Matlab style quantile function of a discrete/continuous distribution
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105
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106 function q = quantile (x, p, dim = 1, method = 5)
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107
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108 if (nargin < 1 || nargin > 4)
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109 print_usage ();
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110 endif
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111
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112 if (nargin < 2)
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113 p = [0.00 0.25, 0.50, 0.75, 1.00];
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114 endif
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115
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116 if (!(isscalar (dim) && dim == fix (dim)) ||
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117 !(1 <= dim && dim <= ndims (x)))
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118 error ("quantile: DIM must be an integer and a valid dimension");
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119 endif
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120
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121 ## Set the permutation vector.
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122 perm = 1:ndims(x);
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123 perm(1) = dim;
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124 perm(dim) = 1;
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125
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126 ## Permute dim to the 1st index.
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127 x = permute (x, perm);
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128
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129 ## Save the size of the permuted x N-d array.
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130 sx = size (x);
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131
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132 ## Reshape to a 2-d array.
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133 x = reshape (x, [sx(1), prod(sx(2:end))]);
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134
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135 ## Calculate the quantiles.
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136 q = __quantile__ (x, p, method);
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137
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138 ## Return the shape to the original N-d array.
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139 q = reshape (q, [numel(p), sx(2:end)]);
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Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
140
8506
bc982528de11 comment style fixes
John W. Eaton <jwe@octave.org>
parents: 7643
diff changeset
141 ## Permute the 1st index back to dim.
7643
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
142 q = ipermute (q, perm);
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
143
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
144 endfunction
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
145
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
146 %!test
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
147 %! p = 0.5;
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
148 %! x = sort (rand (11));
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
149 %! q = quantile (x, p);
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
150 %! assert (q, x(6,:))
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
151 %! x = x.';
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
152 %! q = quantile (x, p, 2);
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
153 %! assert (q, x(:,6));
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
154
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
155 %!test
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
156 %! 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
157 %! x = [1; 2; 3; 4];
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
158 %! 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
159 %! 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
160 %! 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
161 %! 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
162 %! 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
163 %! 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
164 %! 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
165 %! 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
166 %! 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
167 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
168 %! q = quantile (x, p, 1, m).';
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
169 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
170 %! endfor
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
171
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
172 %!test
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
173 %! 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
174 %! x = [1; 2; 3; 4; 5];
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
175 %! 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
176 %! 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
177 %! 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
178 %! 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
179 %! 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
180 %! 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
181 %! 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
182 %! 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
183 %! 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
184 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
185 %! q = quantile (x, p, 1, m).';
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
186 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
187 %! endfor
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
188
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
189 %!test
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
190 %! 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
191 %! x = [1; 2; 5; 9];
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
192 %! 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
193 %! 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
194 %! 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
195 %! 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
196 %! 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
197 %! 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
198 %! 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
199 %! 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
200 %! 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
201 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
202 %! q = quantile (x, p, 1, m).';
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
203 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
204 %! endfor
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
205
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
206 %!test
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
207 %! 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
208 %! x = [1; 2; 5; 9; 11];
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
209 %! 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
210 %! 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
211 %! 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
212 %! 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
213 %! 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
214 %! 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
215 %! 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
216 %! 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
217 %! 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
218 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
219 %! q = quantile (x, p, 1, m).';
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
220 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
221 %! endfor
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
222
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
223 %!test
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
224 %! 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
225 %! 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
226 %! 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
227 %! 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
228 %! 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
229 %! 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
230 %! 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
231 %! 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
232 %! 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
233 %! 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
234 %! 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
235 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
236 %! q = quantile (x, p, 1, m).';
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
237 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
238 %! endfor
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
239
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
240 %!test
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
241 %! 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
242 %! 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
243 %! -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
244 %! 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
245 %! -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
246 %! -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
247 %! -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
248 %! -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
249 %! -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
250 %! -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
251 %! -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
252 %! -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
253 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
254 %! q = quantile (x, p, 1, m).';
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
255 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
256 %! endfor
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
257
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
258 %!test
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
259 %! p = 0.5;
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
260 %! 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
261 %! 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
262 %! 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
263 %! 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
264 %! 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
265 %! tol = 0.00001;
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
266 %! x(5,5) = NaN;
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
267 %! 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
268 %! x(1,1) = NaN;
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
269 %! 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
270 %! x(3,3) = NaN;
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
271 %! 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
272
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
273 %!test
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
274 %! sx = [2, 3, 4];
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
275 %! x = rand (sx);
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
276 %! dim = 2;
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
277 %! p = 0.5;
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
278 %! yobs = quantile (x, p, dim);
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
279 %! yexp = median (x, dim);
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
280 %! assert (yobs, yexp);
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
281
11436
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 11131
diff changeset
282 %% Test input validation
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283 %!error quantile ()
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284 %!error quantile (1, 2, 3, 4, 5)
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285 %!error quantile (1, 1, 1.5)
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286 %!error quantile (1, 1, 0)
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287 %!error quantile (1, 1, 3)
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288
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289 ## For the cumulative probability values in @var{p}, compute the
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290 ## quantiles, @var{q} (the inverse of the cdf), for the sample, @var{x}.
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291 ##
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292 ## The optional input, @var{method}, refers to nine methods available in R
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293 ## (http://www.r-project.org/). The default is @var{method} = 7. For more
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294 ## detail, see `help quantile'.
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295 ## @seealso{prctile, quantile, statistics}
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296
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297 ## Author: Ben Abbott <bpabbott@mac.com>
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298 ## Vectorized version: Jaroslav Hajek <highegg@gmail.com>
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299 ## Description: Quantile function of empirical samples
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300
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301 function inv = __quantile__ (x, p, method = 5)
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302
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303 if (nargin < 2 || nargin > 3)
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304 print_usage ();
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305 endif
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306
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307 if (!isnumeric (x))
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308 error ("quantile: X must be a numeric vector or matrix");
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309 endif
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310
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311 ## Save length and set shape of quantiles.
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312 n = numel (p);
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313 p = p(:);
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314
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315 ## Save length and set shape of samples.
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316 ## FIXME: does sort guarantee that NaN's come at the end?
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317 x = sort (x);
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318 m = sum (! isnan (x));
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319 mx = size (x, 1);
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320 nx = size (x, 2);
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321
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322 ## Initialize output values.
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323 inv = Inf*(-(p < 0) + (p > 1));
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324 inv = repmat (inv, 1, nx);
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325
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326 ## Do the work.
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327 if (any(k = find((p >= 0) & (p <= 1))))
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328 n = length (k);
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329 p = p (k);
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330 ## Special case.
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331 if (mx == 1)
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332 inv(k,:) = repmat (x, n, 1);
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333 return
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334 endif
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335
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336 ## The column-distribution indices.
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337 pcd = kron (ones (n, 1), mx*(0:nx-1));
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338 mm = kron (ones (n, 1), m);
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339 switch (method)
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340 case {1, 2, 3}
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341 switch (method)
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342 case 1
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343 p = max (ceil (kron (p, m)), 1);
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344 inv(k,:) = x(p + pcd);
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345
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346 case 2
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347 p = kron (p, m);
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348 p_lr = max (ceil (p), 1);
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349 p_rl = min (floor (p + 1), mm);
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350 inv(k,:) = (x(p_lr + pcd) + x(p_rl + pcd))/2;
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351
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352 case 3
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353 ## Used by SAS, method PCTLDEF=2.
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354 ## http://support.sas.com/onlinedoc/913/getDoc/en/statug.hlp/stdize_sect14.htm
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355 t = max (kron (p, m), 1);
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356 t = roundb (t);
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357 inv(k,:) = x(t + pcd);
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358 endswitch
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359
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360 otherwise
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361 switch (method)
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362 case 4
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363 p = kron (p, m);
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364
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365 case 5
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366 ## Used by Matlab.
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367 p = kron (p, m) + 0.5;
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368
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369 case 6
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370 ## Used by Minitab and SPSS.
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371 p = kron (p, m+1);
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372
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373 case 7
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374 ## Used by S and R.
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375 p = kron (p, m-1) + 1;
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376
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377 case 8
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378 ## Median unbiased .
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379 p = kron (p, m+1/3) + 1/3;
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380
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381 case 9
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382 ## Approximately unbiased respecting order statistics.
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383 p = kron (p, m+0.25) + 0.375;
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384
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385 otherwise
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386 error ("quantile: Unknown METHOD, '%d'", method);
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387 endswitch
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388
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389 ## Duplicate single values.
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390 imm1 = mm == 1;
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391 x(2,imm1) = x(1,imm1);
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392
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393 ## Interval indices.
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394 pi = max (min (floor (p), mm-1), 1);
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395 pr = max (min (p - pi, 1), 0);
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396 pi += pcd;
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397 inv(k,:) = (1-pr) .* x(pi) + pr .* x(pi+1);
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398 endswitch
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399 endif
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400
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401 endfunction
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402