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
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1 ## Copyright (C) 1995-2017 Kurt Hornik
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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
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8 ## (at 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
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13 ## GNU 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 ## <https://www.gnu.org/licenses/>.
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18
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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
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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 ##
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48 ## The argument @var{opt} determines the type of normalization to use.
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49 ## Valid values are
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50 ##
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51 ## @table @asis
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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 ##
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56 ## @item 1:
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57 ## normalizes with @math{N}, this provides the second moment around the mean
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58 ## @end table
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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}
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65 ## @end deftypefn
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66
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67 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
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68 ## Description: Compute variance
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69
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70 function retval = var (x, opt = 0, dim)
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71
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72 if (nargin < 1 || nargin > 3)
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73 print_usage ();
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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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88 if (nargin < 3)
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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");
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94 endif
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95 endif
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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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108 endif
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109
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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)