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[Octave-cvsupdate] SF.net SVN: octave:[5636] trunk/octave-forge/main/statistics
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From: <te...@us...> - 2009-03-24 17:40:51
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Revision: 5636
http://octave.svn.sourceforge.net/octave/?rev=5636&view=rev
Author: tealev
Date: 2009-03-24 17:40:40 +0000 (Tue, 24 Mar 2009)
Log Message:
-----------
Confidence level of a sampled multinomial distribution.
Modified Paths:
--------------
trunk/octave-forge/main/statistics/INDEX
Added Paths:
-----------
trunk/octave-forge/main/statistics/inst/cl_multinom.m
Modified: trunk/octave-forge/main/statistics/INDEX
===================================================================
--- trunk/octave-forge/main/statistics/INDEX 2009-03-24 17:14:47 UTC (rev 5635)
+++ trunk/octave-forge/main/statistics/INDEX 2009-03-24 17:40:40 UTC (rev 5636)
@@ -25,6 +25,7 @@
jsucdf
jsupdf
random
+ cl_multinom
Descriptive statistics
nansum
nanmax
Added: trunk/octave-forge/main/statistics/inst/cl_multinom.m
===================================================================
--- trunk/octave-forge/main/statistics/inst/cl_multinom.m (rev 0)
+++ trunk/octave-forge/main/statistics/inst/cl_multinom.m 2009-03-24 17:40:40 UTC (rev 5636)
@@ -0,0 +1,124 @@
+# -*- texinfo -*-
+#
+# @deftypefn {Function File} {@var{CL}} cl_multinom( @var{x},@var{N},@var{b},@var{calculation_type} ) - Confidence level of multinomial portions
+# Returns confidence level of multinomial parameters estimated @math{ p = x / sum(x) } with predefined confidence interval @var{b}.
+# Finite population is also considered.
+#
+# This function calculates the level of confidence at which the samples represent the true distribution
+# given that there is a predefined tolerance (confidence interval).
+# This is the upside down case of the typical excercises at which we want to get the confidence interval
+# given the confidence level (and the estimated parameters of the underlying distribution).
+# But once we accept (lets say at elections) that we have a standard predefined
+# maximal acceptable error rate (e.g. @var{b}=0.02 ) in the estimation and we just want to know that how sure we
+# can be that the measured proportions are the same as in the
+# entire population (ie. the expected value and mean of the samples are roghly the same) we need to use this function.
+#
+# @subheading Arguments
+# @itemize @bullet
+# @item @var{x} : int vector : sample frequencies bins
+# @item @var{N} : int : Population size that was sampled by x. If N<sum(x), infinite number assumed
+# @item @var{b} : real, vector : confidence interval
+# if vector, it should be the size of x containing confence interval for each cells
+# if scalar, each cell will have the same value of b unless it is zero or -1
+# if value is 0, b=.02 is assumed which is standard choice at elections
+# otherwise it is calculated in a way that one sample in a cell alteration defines the confidence interval
+# @item @var{calculation_type} : string : (Optional), described below
+# "bromaghin" (default) - do not change it unless you have a good reason to do so
+# "cochran"
+# "agresti_cull" this is not exactly the solution at reference given below but an adjustment of the solutions above
+# @end itemize
+#
+# @subheading Returns
+# Confidence level.
+#
+# @subheading Example
+# CL = cl_multinom( [27;43;19;11], 10000, 0.05 )
+# returns 0.69 confidence level.
+#
+# @subheading References
+#
+# "bromaghin" calculation type (default) is based on
+# is based on the article
+# Jeffrey F. Bromaghin, "Sample Size Determination for Interval Estimation of Multinomial Probabilities", The American Statistician vol 47, 1993, pp 203-206.
+#
+# "cochran" calculation type
+# is based on article
+# Robert T. Tortora, "A Note on Sample Size Estimation for Multinomial Populations", The American Statistician, , Vol 32. 1978, pp 100-102.
+#
+# "agresti_cull" calculation type
+# is based on article in which Quesenberry Hurst and Goodman result is combined
+# A. Agresti and B.A. Coull, "Approximate is better than \"exact\" for interval estimation of binomial portions", The American Statistician, Vol. 52, 1998, pp 119-126
+#
+# @end deftypefn
+
+
+# Copyright (C) 2009 Levente Torok / Tor...@gm...
+# 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 2 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/>.
+#
+
+function CL = cl_multinom( x, N, b, calculation_type )
+
+ k = rows(x);
+ nn = sum(x);
+ p = x / nn;
+
+ if (nargin < 3)
+ b = .05;
+ endif
+ if (isscalar( b ))
+ if (b==0) b=0.02; endif
+ b = ones( rows(x), 1 ) * b;
+
+ if (b<0) b=1 ./ max( x, 1 ); endif
+ endif
+ bb = b .* b;
+
+ if (N==nn)
+ CL = 1;
+ return;
+ endif
+
+ if (N<nn)
+ fpc = 1;
+ else
+ fpc = (N-1) / (N-nn); # finite population correction tag
+ endif
+
+ beta = p.*(1-p);
+
+ if ( nargin < 4 )
+ calculation_type = "bromaghin";
+ endif
+
+ switch calculation_type
+ case {"cochran"}
+ t = sqrt( fpc * nn * bb ./ beta )
+ alpha = ( 1 - normcdf( t )) * 2
+
+ case {"bromaghin"}
+ t = sqrt( fpc * (nn * 2 * bb )./ ( beta - 2 * bb + sqrt( beta .* beta - bb .* ( 4*beta - 1 ))) );
+ alpha = ( 1 - normcdf( t )) * 2;
+
+ case {"agresti_cull"}
+ ts = fpc * nn * bb ./ beta ;
+ if ( k<=2 )
+ alpha = 1 - chi2cdf( ts, k-1 ); % adjusted Wilson interval
+ else
+ alpha = 1 - chi2cdf( ts/k, 1 ); % Goodman interval with Bonferroni argument
+ endif
+ endswitch
+
+ CL = 1 - max( alpha );
+
+endfunction
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