1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
|
## Copyright (C) 1995-2013 Kurt Hornik
##
## This file is part of Octave.
##
## Octave is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or (at
## your option) any later version.
##
## Octave is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} statistics (@var{x})
## @deftypefnx {Function File} {} statistics (@var{x}, @var{dim})
## Return a vector with the minimum, first quartile, median, third quartile,
## maximum, mean, standard deviation, skewness, and kurtosis of the elements of
## the vector @var{x}.
##
## If @var{x} is a matrix, calculate statistics over the first
## non-singleton dimension.
## If the optional argument @var{dim} is given, operate along this dimension.
## @seealso{min, max, median, mean, std, skewness, kurtosis}
## @end deftypefn
## Author: KH <Kurt.Hornik@wu-wien.ac.at>
## Description: Compute basic statistics
function stats = statistics (x, dim)
if (nargin != 1 && nargin != 2)
print_usage ();
endif
if (! (isnumeric (x) || islogical (x)))
error ("statistics: X must be a numeric vector or matrix");
endif
nd = ndims (x);
sz = size (x);
if (nargin != 2)
## Find the first non-singleton dimension.
(dim = find (sz > 1, 1)) || (dim = 1);
else
if (!(isscalar (dim) && dim == fix (dim))
|| !(1 <= dim && dim <= nd))
error ("statistics: DIM must be an integer and a valid dimension");
endif
endif
if (sz(dim) < 2)
error ("statistics: dimension of X is too small (<2)");
endif
emp_inv = quantile (x, [0.25; 0.5; 0.75], dim, 7);
stats = cat (dim, min (x, [], dim), emp_inv, max (x, [], dim), mean (x, dim),
std (x, [], dim), skewness (x, [], dim), kurtosis (x, [], dim));
endfunction
%!test
%! x = rand (7,5);
%! s = statistics (x);
%! assert (min (x), s(1,:), eps);
%! assert (median (x), s(3,:), eps);
%! assert (max (x), s(5,:), eps);
%! assert (mean (x), s(6,:), eps);
%! assert (std (x), s(7,:), eps);
%! assert (skewness (x), s(8,:), eps);
%! assert (kurtosis (x), s(9,:), eps);
%! x = rand (7,5);
%! s = statistics (x, 2);
%! assert (min (x, [], 2), s(:,1), eps);
%! assert (median (x, 2), s(:,3), eps);
%! assert (max (x, [], 2), s(:,5), eps);
%! assert (mean (x, 2), s(:,6), eps);
%! assert (std (x, [], 2), s(:,7), eps);
%! assert (skewness (x, [], 2), s(:,8), eps);
%! assert (kurtosis (x, [], 2), s(:,9), eps);
%% Test input validation
%!error statistics ()
%!error statistics (1, 2, 3)
%!error statistics (['A'; 'B'])
%!error statistics (1, ones (2,2))
%!error statistics (1, 1.5)
%!error statistics (1, 0)
%!error statistics (1, 3)
%!error statistics (1)
|
