Mercurial > octave-nkf
annotate scripts/statistics/base/kendall.m @ 10793:be55736a0783
Grammarcheck the documentation from m-files.
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Sun, 18 Jul 2010 20:35:16 -0700 |
| parents | f0c3d3fc4903 |
| children | 693e22af08ae |
| rev | line source |
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| 8920 | 1 ## Copyright (C) 1995, 1996, 1997, 1998, 2000, 2002, 2005, 2006, 2007, 2009 |
| 7017 | 2 ## Kurt Hornik |
| 3426 | 3 ## |
| 3922 | 4 ## This file is part of Octave. |
| 5 ## | |
| 6 ## Octave is free software; you can redistribute it and/or modify it | |
| 7 ## under the terms of the GNU General Public License as published by | |
| 7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
| 9 ## your option) any later version. | |
| 3426 | 10 ## |
| 3922 | 11 ## Octave is distributed in the hope that it will be useful, but |
| 3200 | 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
| 13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 3426 | 14 ## General Public License for more details. |
| 15 ## | |
| 3200 | 16 ## You should have received a copy of the GNU General Public License |
| 7016 | 17 ## along with Octave; see the file COPYING. If not, see |
| 18 ## <http://www.gnu.org/licenses/>. | |
| 3200 | 19 |
| 3453 | 20 ## -*- texinfo -*- |
| 21 ## @deftypefn {Function File} {} kendall (@var{x}, @var{y}) | |
| 22 ## Compute Kendall's @var{tau} for each of the variables specified by | |
| 23 ## the input arguments. | |
| 3200 | 24 ## |
| 25 ## For matrices, each row is an observation and each column a variable; | |
| 26 ## vectors are always observations and may be row or column vectors. | |
| 27 ## | |
| 3453 | 28 ## @code{kendall (@var{x})} is equivalent to @code{kendall (@var{x}, |
| 29 ## @var{x})}. | |
| 30 ## | |
| 31 ## For two data vectors @var{x}, @var{y} of common length @var{n}, | |
| 32 ## Kendall's @var{tau} is the correlation of the signs of all rank | |
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33 ## differences of @var{x} and @var{y}; i.e., if both @var{x} and |
| 3453 | 34 ## @var{y} have distinct entries, then |
| 3200 | 35 ## |
| 3453 | 36 ## @tex |
| 37 ## $$ \tau = {1 \over n(n-1)} \sum_{i,j} {\rm sign}(q_i-q_j) {\rm sign}(r_i-r_j) $$ | |
| 38 ## @end tex | |
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39 ## @ifnottex |
| 3453 | 40 ## @example |
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41 ## @group |
| 3453 | 42 ## 1 |
| 43 ## tau = ------- SUM sign (q(i) - q(j)) * sign (r(i) - r(j)) | |
| 44 ## n (n-1) i,j | |
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45 ## @end group |
| 3453 | 46 ## @end example |
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47 ## @end ifnottex |
| 3200 | 48 ## |
| 3453 | 49 ## @noindent |
| 50 ## in which the | |
| 51 ## @tex | |
| 52 ## $q_i$ and $r_i$ | |
| 53 ## @end tex | |
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54 ## @ifnottex |
| 3453 | 55 ## @var{q}(@var{i}) and @var{r}(@var{i}) |
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56 ## @end ifnottex |
| 3453 | 57 ## are the ranks of |
| 58 ## @var{x} and @var{y}, respectively. | |
| 59 ## | |
| 60 ## If @var{x} and @var{y} are drawn from independent distributions, | |
| 61 ## Kendall's @var{tau} is asymptotically normal with mean 0 and variance | |
| 6754 | 62 ## @tex |
| 63 ## ${2 (2n+5) \over 9n(n-1)}$. | |
| 64 ## @end tex | |
| 65 ## @ifnottex | |
| 3453 | 66 ## @code{(2 * (2@var{n}+5)) / (9 * @var{n} * (@var{n}-1))}. |
| 6754 | 67 ## @end ifnottex |
| 3453 | 68 ## @end deftypefn |
| 3200 | 69 |
| 5428 | 70 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 3456 | 71 ## Description: Kendall's rank correlation tau |
| 3200 | 72 |
| 73 function tau = kendall (x, y) | |
| 3426 | 74 |
| 3200 | 75 if ((nargin < 1) || (nargin > 2)) |
| 6046 | 76 print_usage (); |
| 3200 | 77 endif |
| 78 | |
| 79 if (rows (x) == 1) | |
| 80 x = x'; | |
| 81 endif | |
| 82 [n, c] = size (x); | |
| 83 | |
| 84 if (nargin == 2) | |
| 85 if (rows (y) == 1) | |
| 86 y = y'; | |
| 87 endif | |
| 88 if (rows (y) != n) | |
| 3456 | 89 error ("kendall: x and y must have the same number of observations"); |
| 3200 | 90 else |
| 91 x = [x, y]; | |
| 92 endif | |
| 93 endif | |
| 3426 | 94 |
| 3200 | 95 r = ranks (x); |
| 96 m = sign (kron (r, ones (n, 1)) - kron (ones (n, 1), r)); | |
| 97 tau = cor (m); | |
| 3426 | 98 |
| 3200 | 99 if (nargin == 2) |
| 100 tau = tau (1 : c, (c + 1) : columns (x)); | |
| 101 endif | |
| 3426 | 102 |
| 6754 | 103 endfunction |