Mercurial > octave
annotate scripts/statistics/var.m @ 24547:fdc9ce839afd
maint: Remove statistics functions which have been shifted to Octave Forge package.
* NEWS: Announce list of functions removed from core.
* scripts/statistics/center.m, scripts/statistics/corr.m,
scripts/statistics/corrcoef.m, scripts/statistics/cov.m,
scripts/statistics/discrete_cdf.m, scripts/statistics/discrete_inv.m,
scripts/statistics/discrete_pdf.m, scripts/statistics/discrete_rnd.m,
scripts/statistics/empirical_cdf.m, scripts/statistics/empirical_inv.m,
scripts/statistics/empirical_pdf.m, scripts/statistics/empirical_rnd.m,
scripts/statistics/histc.m, scripts/statistics/iqr.m,
scripts/statistics/kendall.m, scripts/statistics/kurtosis.m,
scripts/statistics/mean.m, scripts/statistics/meansq.m,
scripts/statistics/median.m, scripts/statistics/mode.m,
scripts/statistics/module.mk, scripts/statistics/moment.m,
scripts/statistics/prctile.m, scripts/statistics/quantile.m,
scripts/statistics/range.m, scripts/statistics/ranks.m,
scripts/statistics/run_count.m, scripts/statistics/runlength.m,
scripts/statistics/skewness.m, scripts/statistics/spearman.m,
scripts/statistics/statistics.m, scripts/statistics/std.m,
scripts/statistics/var.m, scripts/statistics/zscore.m:
Moved from scripts/statistics/base.
* scripts/module.mk: Update build system. Remove @include for directories
base/, tests/, models/, distributions/.
* octave.texi: Update @detailmenu.
* stats.txi: Rewrite statistics chapter with condensed list of functions.
* scripts/statistics/base/module.mk,
scripts/statistics/distributions/module.mk, scripts/statistics/models/module.mk
scripts/statistics/tests/module.mk:
Removed from build system.
* scripts/statistics/base/cloglog.m, scripts/statistics/base/crosstab.m,
scripts/statistics/base/logit.m, scripts/statistics/base/moment.m,
scripts/statistics/base/ppplot.m, scripts/statistics/base/probit.m,
scripts/statistics/base/qqplot.m, scripts/statistics/distributions/betacdf.m,
scripts/statistics/distributions/betainv.m,
scripts/statistics/distributions/betapdf.m,
scripts/statistics/distributions/betarnd.m,
scripts/statistics/distributions/binocdf.m,
scripts/statistics/distributions/binoinv.m,
scripts/statistics/distributions/binopdf.m,
scripts/statistics/distributions/binornd.m,
scripts/statistics/distributions/cauchy_cdf.m,
scripts/statistics/distributions/cauchy_inv.m,
scripts/statistics/distributions/cauchy_pdf.m,
scripts/statistics/distributions/cauchy_rnd.m,
scripts/statistics/distributions/chi2cdf.m,
scripts/statistics/distributions/chi2inv.m,
scripts/statistics/distributions/chi2pdf.m,
scripts/statistics/distributions/chi2rnd.m,
scripts/statistics/distributions/discrete_cdf.m,
scripts/statistics/distributions/discrete_inv.m,
scripts/statistics/distributions/discrete_pdf.m,
scripts/statistics/distributions/discrete_rnd.m,
scripts/statistics/distributions/empirical_cdf.m,
scripts/statistics/distributions/empirical_inv.m,
scripts/statistics/distributions/empirical_pdf.m,
scripts/statistics/distributions/empirical_rnd.m,
scripts/statistics/distributions/expcdf.m,
scripts/statistics/distributions/expinv.m,
scripts/statistics/distributions/exppdf.m,
scripts/statistics/distributions/exprnd.m,
scripts/statistics/distributions/fcdf.m,
scripts/statistics/distributions/finv.m,
scripts/statistics/distributions/fpdf.m,
scripts/statistics/distributions/frnd.m,
scripts/statistics/distributions/gamcdf.m,
scripts/statistics/distributions/gaminv.m,
scripts/statistics/distributions/gampdf.m,
scripts/statistics/distributions/gamrnd.m,
scripts/statistics/distributions/geocdf.m,
scripts/statistics/distributions/geoinv.m,
scripts/statistics/distributions/geopdf.m,
scripts/statistics/distributions/geornd.m,
scripts/statistics/distributions/hygecdf.m,
scripts/statistics/distributions/hygeinv.m,
scripts/statistics/distributions/hygepdf.m,
scripts/statistics/distributions/hygernd.m,
scripts/statistics/distributions/kolmogorov_smirnov_cdf.m,
scripts/statistics/distributions/laplace_cdf.m,
scripts/statistics/distributions/laplace_inv.m,
scripts/statistics/distributions/laplace_pdf.m,
scripts/statistics/distributions/laplace_rnd.m,
scripts/statistics/distributions/logistic_cdf.m,
scripts/statistics/distributions/logistic_inv.m,
scripts/statistics/distributions/logistic_pdf.m,
scripts/statistics/distributions/logistic_rnd.m,
scripts/statistics/distributions/logncdf.m,
scripts/statistics/distributions/logninv.m,
scripts/statistics/distributions/lognpdf.m,
scripts/statistics/distributions/lognrnd.m,
scripts/statistics/distributions/nbincdf.m,
scripts/statistics/distributions/nbininv.m,
scripts/statistics/distributions/nbinpdf.m,
scripts/statistics/distributions/nbinrnd.m,
scripts/statistics/distributions/normcdf.m,
scripts/statistics/distributions/norminv.m,
scripts/statistics/distributions/normpdf.m,
scripts/statistics/distributions/normrnd.m,
scripts/statistics/distributions/poisscdf.m,
scripts/statistics/distributions/poissinv.m,
scripts/statistics/distributions/poisspdf.m,
scripts/statistics/distributions/poissrnd.m,
scripts/statistics/distributions/stdnormal_cdf.m,
scripts/statistics/distributions/stdnormal_inv.m,
scripts/statistics/distributions/stdnormal_pdf.m,
scripts/statistics/distributions/stdnormal_rnd.m,
scripts/statistics/distributions/tcdf.m,
scripts/statistics/distributions/tinv.m,
scripts/statistics/distributions/tpdf.m,
scripts/statistics/distributions/trnd.m,
scripts/statistics/distributions/unidcdf.m,
scripts/statistics/distributions/unidinv.m,
scripts/statistics/distributions/unidpdf.m,
scripts/statistics/distributions/unidrnd.m,
scripts/statistics/distributions/unifcdf.m,
scripts/statistics/distributions/unifinv.m,
scripts/statistics/distributions/unifpdf.m,
scripts/statistics/distributions/unifrnd.m,
scripts/statistics/distributions/wblcdf.m,
scripts/statistics/distributions/wblinv.m,
scripts/statistics/distributions/wblpdf.m,
scripts/statistics/distributions/wblrnd.m,
scripts/statistics/distributions/wienrnd.m,
scripts/statistics/models/logistic_regression.m,
scripts/statistics/models/private/logistic_regression_derivatives.m,
scripts/statistics/models/private/logistic_regression_likelihood.m,
scripts/statistics/tests/anova.m, scripts/statistics/tests/bartlett_test.m,
scripts/statistics/tests/chisquare_test_homogeneity.m,
scripts/statistics/tests/chisquare_test_independence.m,
scripts/statistics/tests/cor_test.m,
scripts/statistics/tests/f_test_regression.m,
scripts/statistics/tests/hotelling_test.m,
scripts/statistics/tests/hotelling_test_2.m,
scripts/statistics/tests/kolmogorov_smirnov_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test_2.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/manova.m, scripts/statistics/tests/mcnemar_test.m,
scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/run_test.m,
scripts/statistics/tests/sign_test.m, scripts/statistics/tests/t_test.m,
scripts/statistics/tests/t_test_2.m,
scripts/statistics/tests/t_test_regression.m,
scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m,
scripts/statistics/tests/welch_test.m,
scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m,
scripts/statistics/tests/z_test_2.m:
Removed functions.
author | Rik <rik@octave.org> |
---|---|
date | Sun, 07 Jan 2018 17:13:23 -0800 |
parents | scripts/statistics/base/var.m@194eb4bd202b |
children | d85b2485af9e |
rev | line source |
---|---|
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1 ## Copyright (C) 1995-2017 Kurt Hornik |
3426 | 2 ## |
3922 | 3 ## This file is part of Octave. |
4 ## | |
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5 ## Octave is free software: you can redistribute it and/or modify it |
3922 | 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 |
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8 ## (at your option) any later version. |
3426 | 9 ## |
3922 | 10 ## Octave is distributed in the hope that it will be useful, but |
3200 | 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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13 ## GNU General Public License for more details. |
3426 | 14 ## |
3200 | 15 ## You should have received a copy of the GNU General Public License |
7016 | 16 ## along with Octave; see the file COPYING. If not, see |
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17 ## <https://www.gnu.org/licenses/>. |
3200 | 18 |
3453 | 19 ## -*- texinfo -*- |
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20 ## @deftypefn {} {} var (@var{x}) |
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21 ## @deftypefnx {} {} var (@var{x}, @var{opt}) |
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22 ## @deftypefnx {} {} var (@var{x}, @var{opt}, @var{dim}) |
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23 ## Compute the variance of the elements of the vector @var{x}. |
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24 ## |
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25 ## The variance is defined as |
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26 ## @tex |
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27 ## $$ |
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28 ## {\rm var} (x) = \sigma^2 = {\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1} |
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29 ## $$ |
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30 ## where $\bar{x}$ is the mean value of @var{x} and $N$ is the number of |
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31 ## elements of @var{x}. |
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32 ## |
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33 ## @end tex |
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34 ## @ifnottex |
4849 | 35 ## |
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36 ## @example |
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37 ## @group |
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38 ## var (@var{x}) = 1/(N-1) SUM_i (@var{x}(i) - mean(@var{x}))^2 |
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39 ## @end group |
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40 ## @end example |
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41 ## |
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42 ## where @math{N} is the length of the @var{x} vector. |
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43 ## |
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44 ## @end ifnottex |
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45 ## If @var{x} is a matrix, compute the variance for each column and return |
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46 ## them in a row vector. |
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47 ## |
5435 | 48 ## The argument @var{opt} determines the type of normalization to use. |
49 ## Valid values are | |
4849 | 50 ## |
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51 ## @table @asis |
4849 | 52 ## @item 0: |
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53 ## normalize with @math{N-1}, provides the best unbiased estimator of the |
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54 ## variance [default] |
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55 ## |
4849 | 56 ## @item 1: |
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57 ## normalizes with @math{N}, this provides the second moment around the mean |
4849 | 58 ## @end table |
59 ## | |
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60 ## If @math{N} is equal to 1 the value of @var{opt} is ignored and |
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61 ## normalization by @math{N} is used. |
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62 ## |
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63 ## If the optional argument @var{dim} is given, operate along this dimension. |
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64 ## @seealso{cov, std, skewness, kurtosis, moment} |
3453 | 65 ## @end deftypefn |
3426 | 66 |
5428 | 67 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
3456 | 68 ## Description: Compute variance |
3200 | 69 |
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70 function retval = var (x, opt = 0, dim) |
3426 | 71 |
4849 | 72 if (nargin < 1 || nargin > 3) |
6046 | 73 print_usage (); |
4849 | 74 endif |
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75 |
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76 if (! (isnumeric (x) || islogical (x))) |
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77 error ("var: X must be a numeric vector or matrix"); |
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78 endif |
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79 |
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80 if (isempty (opt)) |
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81 opt = 0; |
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82 elseif (opt != 0 && opt != 1) |
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83 error ("var: normalization OPT must be 0 or 1"); |
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84 endif |
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85 |
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86 nd = ndims (x); |
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87 sz = size (x); |
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89 ## Find the first non-singleton dimension. |
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90 (dim = find (sz > 1, 1)) || (dim = 1); |
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91 else |
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92 if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) |
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93 error ("var: DIM must be an integer and a valid dimension"); |
4849 | 94 endif |
95 endif | |
3426 | 96 |
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97 n = size (x, dim); |
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98 if (n == 1) |
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99 if (isa (x, "single")) |
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100 retval = zeros (sz, "single"); |
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101 else |
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102 retval = zeros (sz); |
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103 endif |
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104 elseif (numel (x) > 0) |
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105 retval = sumsq (center (x, dim), dim) / (n - 1 + opt); |
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106 else |
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107 error ("var: X must not be empty"); |
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3200 | 110 endfunction |
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111 |
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112 |
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113 %!assert (var (13), 0) |
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114 %!assert (var (single (13)), single (0)) |
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115 %!assert (var ([1,2,3]), 1) |
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116 %!assert (var ([1,2,3], 1), 2/3, eps) |
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117 %!assert (var ([1,2,3], [], 1), [0,0,0]) |
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118 %!assert (var ([1,2,3], [], 3), [0,0,0]) |
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119 |
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120 ## Test input validation |
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121 %!error var () |
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122 %!error var (1,2,3,4) |
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123 %!error <X must be a numeric> var (['A'; 'B']) |
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124 %!error <OPT must be 0 or 1> var (1, -1) |
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125 %!error <FLAG must be 0 or 1> skewness (1, 2) |
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126 %!error <FLAG must be 0 or 1> skewness (1, [1 0]) |
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127 %!error <DIM must be an integer> var (1, [], ones (2,2)) |
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128 %!error <DIM must be an integer> var (1, [], 1.5) |
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129 %!error <DIM must be .* a valid dimension> var (1, [], 0) |
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130 %!error <X must not be empty> var ([], 1) |