Mercurial > forge
changeset 11638:fa3590906cc5 octave-forge
new runstest function
| author | nir-krakauer |
|---|---|
| date | Wed, 17 Apr 2013 20:23:54 +0000 |
| parents | b6c98205144a |
| children | f2dd6a3d0284 |
| files | main/statistics/INDEX main/statistics/NEWS main/statistics/inst/runstest.m |
| diffstat | 3 files changed, 109 insertions(+), 1 deletions(-) [+] |
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--- a/main/statistics/INDEX Wed Apr 17 19:34:44 2013 +0000 +++ b/main/statistics/INDEX Wed Apr 17 20:23:54 2013 +0000 @@ -68,6 +68,7 @@ hmmestimate hmmgenerate hmmviterbi Hypothesis testing anderson_darling_test + runstest Fitting gamfit Clustering
--- a/main/statistics/NEWS Wed Apr 17 19:34:44 2013 +0000 +++ b/main/statistics/NEWS Wed Apr 17 20:23:54 2013 +0000 @@ -3,7 +3,7 @@ ** The following functions are new: - pcares pcacov stepwisefit hist3 + pcares pcacov runstest stepwisefit hist3 ** dendogram now returns the leaf node numbers and order that the nodes were displayed in.
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/statistics/inst/runstest.m Wed Apr 17 20:23:54 2013 +0000 @@ -0,0 +1,107 @@ +## Copyright (C) 2013 Nir Krakauer <nkrakauer@ccny.cuny.edu> +## +## This program 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. +## +## This program 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 +## this program; if not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{h}, @var{p}, @var{stats} =} runstest (@var{x}, @var{v}) +## Runs test for detecting serial correlation in the vector @var{x}. +## +## @subheading Arguments +## +## @itemize @bullet +## @item +## @var{x} is the vector of given values. +## @item +## @var{v} is the value to subtract from @var{x} to get runs (defaults to @code{median(x)}) +## @end itemize +## +## @subheading Return values +## +## @itemize @bullet +## @item +## @var{h} is true if serial correlation is detected at the 95% confidence level (two-tailed), false otherwise. +## @item +## @var{p} is the probablity of obtaining a test statistic of the magnitude found under the null hypothesis of no serial correlation. +## @item +## @var{stats} is the structure containing as fields the number of runs @var{nruns}; the numbers of positive and negative values of @code{x - v}, @var{n1} and @var{n0}; and the test statistic @var{z}. +## +## @end itemize +## +## Note: the large-sample normal approximation is used to find @var{h} and @var{p}. This is accurate if @var{n1}, @var{n0} are both greater than 10. +## +## Reference: +## NIST Engineering Statistics Handbook, 1.3.5.13. Runs Test for Detecting Non-randomness, http://www.itl.nist.gov/div898/handbook/eda/section3/eda35d.htm +## +## @seealso{} +## @end deftypefn + +## Author: Nir Krakauer <nkrakauer@ccny.cuny.edu> +## Description: Runs test for detecting serial correlation + +function [h, p, stats] = runstest (x, x2) + + # Check arguments + if (nargin < 1) + print_usage; + endif + + if nargin > 1 && isnumeric(x2) + v = x2; + else + v = median(x); + endif + + x = x(~isnan(x)); #delete missing values + x = sign(x - v); + x = x(x ~= 0); #delete any zeros + + R = sum((x(1:(end-1)) .* x(2:end)) < 0) + 1; #number of runs + + #expected number of runs for an iid sequence + n1 = sum(x > 0); + n2 = sum(x < 0); + R_bar = 1 + 2*n1*n2/(n1 + n2); + + #standard deviation of number of runs for an iid sequence + s_R = sqrt(2*n1*n2*(2*n1*n2 - n1 - n2)/((n1 + n2)^2 * (n1 + n2 - 1))); + + #desired significance level + alpha = 0.05; + + Z = (R - R_bar) / s_R; #test statistic + + p = 2 * normcdf(-abs(Z)); + + h = p < alpha; + + if nargout > 2 + stats.nruns = R; + stats.n1 = n1; + stats.n0 = n2; + stats.z = Z; + endif + +endfunction + + + +%!test +%! data = [-213 -564 -35 -15 141 115 -420 -360 203 -338 -431 194 -220 -513 154 -125 -559 92 -21 -579 -52 99 -543 -175 162 -457 -346 204 -300 -474 164 -107 -572 -8 83 -541 -224 180 -420 -374 201 -236 -531 83 27 -564 -112 131 -507 -254 199 -311 -495 143 -46 -579 -90 136 -472 -338 202 -287 -477 169 -124 -568 17 48 -568 -135 162 -430 -422 172 -74 -577 -13 92 -534 -243 194 -355 -465 156 -81 -578 -64 139 -449 -384 193 -198 -538 110 -44 -577 -6 66 -552 -164 161 -460 -344 205 -281 -504 134 -28 -576 -118 156 -437 -381 200 -220 -540 83 11 -568 -160 172 -414 -408 188 -125 -572 -32 139 -492 -321 205 -262 -504 142 -83 -574 0 48 -571 -106 137 -501 -266 190 -391 -406 194 -186 -553 83 -13 -577 -49 103 -515 -280 201 300 -506 131 -45 -578 -80 138 -462 -361 201 -211 -554 32 74 -533 -235 187 -372 -442 182 -147 -566 25 68 -535 -244 194 -351 -463 174 -125 -570 15 72 -550 -190 172 -424 -385 198 -218 -536 96]; #NIST beam deflection data, http://www.itl.nist.gov/div898/handbook/eda/section4/eda425.htm +%! [h, p, stats] = runstest (data); +%! expected_h = true; +%! expected_p = 0.0070646; +%! expected_z = 2.6938; +%! assert (h, expected_h); +%! assert (p, expected_p, 1E-6); +%! assert (stats.z, expected_z, 1E-4);