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Modified statistics to calculate consistent median.
author Ben Abbott <bpabbott@mac.com>
date Tue, 25 Mar 2008 23:57:49 -0400
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children bc982528de11
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7643
0220da981c2a Modified statistics to calculate consistent median.
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1 ## Copyright (C) 2008 Ben Abbott
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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) of
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25 ## @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 percentiles 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). In the
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34 ## instance that @var{x} is a N-d array, @var{dim} defaults to the first
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35 ## dimension whose size greater than unity.
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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 ## @item Method 2: Similar to method 1 but with averaging at discontinuities.
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45 ## @item Method 3: SAS definition: nearest even order statistic.
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46 ## @end enumerate
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47 ##
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48 ## Continuous sample quantile methods 4 through 9, where p(k) is the linear
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49 ## interpolation function respecting each methods' representative cdf.
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50 ##
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51 ## @enumerate 4
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52 ## @item Method 4: p(k) = k / n. That is, linear interpolation of the empirical cdf.
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53 ## @item Method 5: p(k) = (k - 0.5) / n. That is a piecewise linear function where
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54 ## the knots are the values midway through the steps of the empirical cdf.
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55 ## @item Method 6: p(k) = k / (n + 1).
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56 ## @item Method 7: p(k) = (k - 1) / (n - 1).
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57 ## @item Method 8: p(k) = (k - 1/3) / (n + 1/3). The resulting quantile estimates
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58 ## are approximately median-unbiased regardless of the distribution of @var{x}.
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59 ## @item Method 9: p(k) = (k - 3/8) / (n + 1/4). The resulting quantile estimates
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60 ## are approximately unbiased for the expected order statistics if @var{x} is
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61 ## normally distributed.
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62 ## @end enumerate
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63 ##
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64 ## Hyndman and Fan (1996) recommend method 8. Maxima, S, and R
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65 ## (versions prior to 2.0.0) use 7 as their default. Minitab and SPSS
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66 ## use method 6. Matlab uses method 5.
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67 ##
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68 ## References:
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69 ##
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70 ## @itemize @bullet
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71 ## @item Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New
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72 ## S Language. Wadsworth & Brooks/Cole.
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73 ##
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74 ## @item Hyndman, R. J. and Fan, Y. (1996) Sample quantiles in
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75 ## statistical packages, American Statistician, 50, 361-365.
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76 ##
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77 ## @item R: A Language and Environment for Statistical Computing;
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78 ## @url{http://cran.r-project.org/doc/manuals/fullrefman.pdf}.
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79 ## @end itemize
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80 ## @end deftypefn
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81
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82 ## Author: Ben Abbott <bpabbott@mac.com>
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83 ## Description: Matlab style quantile function of a discrete/continuous distribution
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84
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85 function q = quantile (x, p, dim, method)
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86
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87 if (nargin < 1 || nargin > 4)
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88 print_usage ();
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89 endif
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90
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91 if (nargin < 2)
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92 p = [0.00 0.25, 0.50, 0.75, 1.00];
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93 endif
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94
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95 if (nargin < 3)
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96 dim = 1;
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97 endif
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98
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99 if (nargin < 4)
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100 method = 5;
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101 endif
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102
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103 if (dim > ndims(x))
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104 error ("quantile: invalid dimension.")
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105 endif
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106
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107 # Set the permutation vector.
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108 perm = 1:ndims(x);
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109 perm(1) = dim;
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110 perm(dim) = 1;
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111
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112 # Permute dim to the 1st index.
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113 x = permute (x, perm);
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114
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115 # Save the size of the permuted x N-d array.
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116 sx = size (x);
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117
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118 # Reshape to a 2-d array.
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119 x = reshape (x, [sx(1), prod(sx(2:end))]);
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120
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121 # Calculate the quantiles.
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122 q = __quantile__ (x, p, method);
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123
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124 # Return the shape to the original N-d array.
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125 q = reshape (q, [numel(p), sx(2:end)]);
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126
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127 # Permute the 1st index back to dim.
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128 q = ipermute (q, perm);
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129
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130 endfunction
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131
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132 %!test
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133 %! p = 0.5;
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134 %! x = sort (rand (11));
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135 %! q = quantile (x, p);
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136 %! assert (q, x(6,:))
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137 %! x = x.';
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138 %! q = quantile (x, p, 2);
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139 %! assert (q, x(:,6));
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140
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141 %!test
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142 %! p = [0.00, 0.25, 0.50, 0.75, 1.00];
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143 %! x = [1; 2; 3; 4];
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144 %! a = [1.0000 1.0000 2.0000 3.0000 4.0000
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145 %! 1.0000 1.5000 2.5000 3.5000 4.0000
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146 %! 1.0000 1.0000 2.0000 3.0000 4.0000
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147 %! 1.0000 1.0000 2.0000 3.0000 4.0000
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148 %! 1.0000 1.5000 2.5000 3.5000 4.0000
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149 %! 1.0000 1.2500 2.5000 3.7500 4.0000
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150 %! 1.0000 1.7500 2.5000 3.2500 4.0000
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151 %! 1.0000 1.4167 2.5000 3.5833 4.0000
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152 %! 1.0000 1.4375 2.5000 3.5625 4.0000];
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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