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annotate scripts/statistics/base/__quantile__.m @ 8664:e07e93c04080

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style fixes
author John W. Eaton <jwe@octave.org>
date Wed, 04 Feb 2009 10:56:23 -0500
parents cf59d542f33e
children 7d48766c21a5
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1 ## Copyright (C) 2008 Ben Abbott, 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{method})
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22 ## For the cumulative probability values in @var{p}, compute the
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23 ## quantiles, @var{q} (the inverse of the cdf), for the sample, @var{x}.
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24 ##
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25 ## The optional input, @var{method}, refers to nine methods available in R
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26 ## (http://www.r-project.org/). The default is @var{method} = 7. For more
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27 ## detail, see `help quantile'.
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28 ## @seealso{prctile, quantile, statistics}
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29 ## @end deftypefn
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30
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31 ## Author: Ben Abbott <bpabbott@mac.com>
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32 ## Vectorized version: Jaroslav Hajek <highegg@gmail.com>
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33 ## Description: Quantile function of a empirical samples
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34
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35 function inv = __quantile__ (x, p, method = 5)
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36
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37 if (nargin < 2 || nargin > 3)
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38 print_usage ();
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39 endif
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40
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41 if (! ismatrix (x))
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42 error ("quantile: x must be a matrix");
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43 endif
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44
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45 ## Save length and set shape of quantiles.
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46 n = numel (p);
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47 p = p(:);
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48
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49 ## Save length and set shape of samples.
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50 ## FIXME: does sort guarantee that NaN's come at the end?
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51 x = sort (x);
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52 m = sum (! isnan (x));
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53 mx = size (x, 1);
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54 nx = size (x, 2);
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55
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56 ## Initialize output values.
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57 inv = Inf*(-(p < 0) + (p > 1));
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58 inv = repmat (inv, 1, nx);
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59
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60 ## Do the work.
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61 if (any(k = find((p >= 0) & (p <= 1))))
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62 n = length (k);
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63 p = p (k);
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64 ## Special case.
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65 if (mx == 1)
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66 inv(k,:) = repmat (x, n, 1);
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67 return
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68 endif
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69
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70 ## The column-distribution indices.
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71 pcd = kron (ones (n, 1), mx*(0:nx-1));
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72 mm = kron (ones (n, 1), m);
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73 switch method
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74 case {1, 2, 3}
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75 switch method
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76 case 1
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77 p = max (ceil (kron (p, m)), 1);
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78 inv(k,:) = x(p + pcd);
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79
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80 case 2
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81 p = kron (p, m);
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82 p_lr = max (ceil (p), 1);
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83 p_rl = min (floor (p + 1), mm);
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84 inv(k,:) = (x(p_lr + pcd) + x(p_rl + pcd))/2;
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85
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86 case 3
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87 ## Used by SAS, method PCTLDEF=2.
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88 ## http://support.sas.com/onlinedoc/913/getDoc/en/statug.hlp/stdize_sect14.htm
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89 t = max (kron (p, m), 1);
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90 t = roundb (t);
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91 inv(k,:) = x(t + pcd);
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92 endswitch
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93
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94 otherwise
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95 switch method
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96 case 4
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97 p = kron (p, m);
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98
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99 case 5
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100 ## Used by Matlab.
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101 p = kron (p, m) + 0.5;
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102
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103 case 6
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104 ## Used by Minitab and SPSS.
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105 p = kron (p, m+1);
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106
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107 case 7
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108 ## Used by S and R.
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109 p = kron (p, m-1) + 1;
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110
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111 case 8
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112 ## Median unbiased .
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113 p = kron (p, m+1/3) + 1/3;
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114
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115 case 9
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116 ## Approximately unbiased respecting order statistics.
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117 p = kron (p, m+0.25) + 0.375;
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118
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119 otherwise
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120 error ("quantile: Unknown method, '%d'", method);
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121 endswitch
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122
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123 ## Duplicate single values.
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124 imm1 = mm == 1;
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125 x(2,imm1) = x(1,imm1);
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126
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127 ## Interval indices.
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128 pi = max (min (floor (p), mm-1), 1);
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129 pr = max (min (p - pi, 1), 0);
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130 pi += pcd;
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131 inv(k,:) = (1-pr) .* x(pi) + pr .* x(pi+1);
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132 endswitch
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133 endif
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134
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135 endfunction
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136
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137 %!test
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138 %! p = 0.5;
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139 %! x = sort (rand (11));
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140 %! q = __quantile__ (x, p);
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141 %! assert (q, x(6,:))
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142
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143 %!test
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144 %! p = [0.00, 0.25, 0.50, 0.75, 1.00];
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145 %! x = [1; 2; 3; 4];
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146 %! a = [1.0000 1.0000 2.0000 3.0000 4.0000
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147 %! 1.0000 1.5000 2.5000 3.5000 4.0000
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148 %! 1.0000 1.0000 2.0000 3.0000 4.0000
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149 %! 1.0000 1.0000 2.0000 3.0000 4.0000
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150 %! 1.0000 1.5000 2.5000 3.5000 4.0000
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151 %! 1.0000 1.2500 2.5000 3.7500 4.0000
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152 %! 1.0000 1.7500 2.5000 3.2500 4.0000
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153 %! 1.0000 1.4167 2.5000 3.5833 4.0000
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154 %! 1.0000 1.4375 2.5000 3.5625 4.0000];
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155 %! for m = (1:9)
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156 %! q = __quantile__ (x, p, m).';
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157 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
158 %! endfor
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
159
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
160 %!test
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
161 %! 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
162 %! x = [1; 2; 3; 4; 5];
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
163 %! 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
164 %! 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
165 %! 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
166 %! 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
167 %! 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
168 %! 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
169 %! 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
170 %! 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
171 %! 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
172 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
173 %! q = __quantile__ (x, p, m).';
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
174 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
175 %! endfor
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
176
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
177 %!test
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
178 %! 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
179 %! x = [1; 2; 5; 9];
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
180 %! 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
181 %! 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
182 %! 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
183 %! 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
184 %! 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
185 %! 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
186 %! 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
187 %! 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
188 %! 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
189 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
190 %! q = __quantile__ (x, p, m).';
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
191 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
192 %! endfor
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
193
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
194 %!test
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
195 %! 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
196 %! x = [1; 2; 5; 9; 11];
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
197 %! 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
198 %! 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
199 %! 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
200 %! 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
201 %! 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
202 %! 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
203 %! 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
204 %! 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
205 %! 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
206 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
207 %! q = __quantile__ (x, p, m).';
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
208 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
209 %! endfor
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
210
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
211 %!test
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
212 %! 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
213 %! 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
214 %! 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
215 %! 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
216 %! 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
217 %! 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
218 %! 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
219 %! 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
220 %! 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
221 %! 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
222 %! 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
223 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
224 %! q = __quantile__ (x, p, m).';
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
225 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
226 %! endfor
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
227
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
228 %!test
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
229 %! 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
230 %! 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
231 %! -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
232 %! 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
233 %! -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
234 %! -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
235 %! -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
236 %! -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
237 %! -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
238 %! -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
239 %! -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
240 %! -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
241 %! for m = (1:9)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
242 %! q = __quantile__ (x, p, m).';
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
243 %! assert (q, a(m,:), 0.0001)
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
244 %! endfor
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
245
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
246 %!test
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
247 %! p = 0.5;
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
248 %! 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
249 %! 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
250 %! 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
251 %! 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
252 %! 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
253 %! tol = 0.00001;
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
254 %! x(5,5) = NaN;
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
255 %! assert (__quantile__ (x, p), [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
256 %! x(1,1) = NaN;
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
257 %! assert (__quantile__ (x, p), [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
258 %! x(3,3) = NaN;
0220da981c2a Modified statistics to calculate consistent median.
Ben Abbott <bpabbott@mac.com>
parents:
diff changeset
259 %! assert (__quantile__ (x, p), [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
260