ltpda: m-toolbox/classes/+utils/@math/kstest.m annotate

author	Daniele Nicolodi <nicolodi@science.unitn.it>
date	Wed, 23 Nov 2011 19:22:13 +0100
parents
children

rev	line source
0 f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1 % KSTEST perform the Kolmogorov - Smirnov statistical hypothesis test
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	4 % DESCRIPTION:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	5 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	6 % Kolmogorov - Smirnov test is typically used to assess if a sample comes
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	7 % from a specific distribution or if two data samples came from the same
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	8 % distribution. The test statistics is d_K = max\|S(x) - K(x)\| where S(x)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	9 % and K(x) are cumulative distribution functions of the two inputs
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	10 % respectively.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	11 % In the case of the test on a single data series:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	12 % - null hypothesis is that the data are a realizations of a random variable
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	13 % which is distributed according to the given probability distribution
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	14 % In the case of the test on two data series:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	15 % - null hypothesis is that the two data series are realizations of the same random variable
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	16 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	17 % CALL:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	18 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	19 % H = utils.math.kstest(y1, y2, alpha, distparams)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	20 % [H] = utils.math.kstest(y1, y2, alpha, distparams)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	21 % [H, KSstatistic] = utils.math.kstest(y1, y2, alpha, distparams)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	22 % [H, KSstatistic, criticalValue] = utils.math.kstest(y1, y2, alpha, distparams)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	23 % [H, KSstatistic, criticalValue] = utils.math.kstest(y1, y2, alpha, distparams, shapeparam)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	24 % [H, KSstatistic, criticalValue, pValue] = utils.math.kstest(y1, y2, alpha, distparams, shapeparam, criticalValue)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	25 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	26 % INPUT:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	27 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	28 % - Y1 are the data we want to test against Y2.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	29 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	30 % - Y2 can be a theoretical distribution or a second set of data. In case
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	31 % of theoretical distribution, Y2 should be a string with the corresponding
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	32 % distribution name. Permitted values are:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	33 % - 'NormDist' Nomal distribution
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	34 % - 'Chi2Dist' Chi square distribution
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	35 % - 'FDist' F distribution
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	36 % - 'GammaDist' Gamma distribution
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	37 % If Y2 is left empty a normal distribution is assumed.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	38 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	39 % - ALPHA is the desired significance level (default = 0.05). It represents
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	40 % the probability of rejecting the null hypothesis when it is true.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	41 % Rejecting the null hypothesis, H0, when it is true is called a Type I
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	42 % Error. Therefore, if the null hypothesis is true , the level of the test,
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	43 % is the probability of a type I error.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	44 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	45 % - DISTPARAMS are the parameters of the chosen theoretical distribution.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	46 % You should not assign this input if Y2 are experimental data. In general
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	47 % DISTPARAMS is a vector containing the following distribution parameters:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	48 % - In case of 'NormDist', DISTPARAMS is a vector containing mean and
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	49 % standard deviation of the normal distribution [mean sigma]. Default [0 1]
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	50 % - In case of 'Chi2Dist' , DISTPARAMS is a number containing containing
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	51 % the degrees of freedom of the chi square distribution [dof]. Default [2]
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	52 % - In case of 'FDist', DISTPARAMS is a vector containing the two degrees
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	53 % of freedom of the F distribution [dof1 dof2]. Default [2 2]
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	54 % - In case of 'GammaDist', DISTPARAMS is a vector containing the shape
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	55 % and scale parameters [k, theta]. Default [2 2]
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	56 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	57 % - SHAPEPARAM In the case of comparison of a data series with a
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	58 % theoretical distribution and the data series is composed of correlated
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	59 % elements. K can be adjusted with a shape parameter in order to recover
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	60 % test fairness [3]. In such a case the test is performed for K' = Phi * K.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	61 % Phi is the corresponding Shape parameter. The shape parameter depends on
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	62 % the correlations and on the significance value. It does not depend on
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	63 % data length. Default [1]
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	64 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	65 % - CRITICALVALUE In case the critical value for the test is available from
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	66 % external calculations, e.g. Monte Carlo simulation, the vale can be input
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	67 % to the method
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	68 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	69 % OUTPUT:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	70 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	71 % - H indicates the result of the hypothesis test:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	72 % H = false => Do not reject the null hypothesis at significance level ALPHA.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	73 % H = true => Reject the null hypothesis at significance level ALPHA.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	74 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	75 % - TEST STATISTIC is the value of d_K = max\|S(x) - K(x)\|.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	76 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	77 % - CRITICAL VALUE is the value of the test statistics corresponding to the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	78 % significance level. CRITICAL VALUE is depending on K, where K is the data length of Y1 if
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	79 % Y2 is a theoretical distribution, otherwise if Y1 and Y2 are two data
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	80 % samples K = n1*n2/(n1 + n2) where n1 and n2 are data length of Y1 and Y2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	81 % respectively. In the case of comparison of a data series with a
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	82 % theoretical distribution and the data series is composed of correlated
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	83 % elements. K can be adjusted with a shape parameter in order to recover
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	84 % test fairness [3]. In such a case the test is performed for K' = Phi * K.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	85 % If TEST STATISTIC > CRITICAL VALUE the null hypothesis is rejected.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	86 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	87 % - P VALUE is the probability value associated to the test statistic.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	88 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	89 % Luigi Ferraioli 17-02-2011
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	90 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	91 % REFERENCES:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	92 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	93 % [1] Massey, F.J., (1951) "The Kolmogorov-Smirnov Test for Goodness of
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	94 % Fit", Journal of the American Statistical Association, 46(253):68-78.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	95 % [2] Miller, L.H., (1956) "Table of Percentage Points of Kolmogorov
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	96 % Statistics", Journal of the American Statistical Association,
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	97 % 51(273):111-121.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	98 % [3] Ferraioli L. et al, to be published.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	99 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	100 % % $Id: kstest.m,v 1.8 2011/07/14 07:09:29 mauro Exp $
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	101 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	102 function [H, KSstatistic, criticalValue, pValue] = kstest(y1, y2, alpha, varargin)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	103
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	104 % check inputs
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	105 if isempty(y2)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	106 y2 = 'normdist'; % set normal distribution as default
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	107 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	108 if isempty(alpha)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	109 alpha = 0.05;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	110 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	111
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	112 if nargin > 3
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	113 dof = varargin{1};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	114 elseif nargin <= 3 && ischar(y2)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	115 switch lower(y2) % assign dof
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	116 case 'fdist'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	117 dof = [2 2];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	118 case 'normdist'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	119 dof = [0 1];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	120 case 'chi2dist'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	121 dof = [2];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	122 case 'gammadist'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	123 dof = [2 2];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	124 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	125 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	126
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	127 shp = 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	128 if nargin > 4
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	129 shp = varargin{2};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	130 if isempty(shp)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	131 shp = 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	132 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	133 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	134
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	135 if nargin > 5
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	136 criticalValue = varargin{3};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	137 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	138 criticalValue = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	139 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	140
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	141 n1 = length(y1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	142
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	143 % get empirical distribution for input data
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	144 [CD1,x1] = utils.math.ecdf(y1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	145
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	146 % check if we have a second dataset or a theoretical distribution as second
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	147 % input
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	148 if ischar(y2)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	149 % switch between theoretical distributions
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	150 switch lower(y2)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	151 case 'fdist'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	152 CD2 = utils.math.Fcdf(x1, dof(1), dof(2));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	153 case 'normdist'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	154 CD2 = utils.math.Normcdf(x1, dof(1), dof(2));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	155 case 'chi2dist'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	156 CD2 = utils.math.Chi2cdf(x1, dof(1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	157 case 'gammadist'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	158 CD2 = gammainc(x./dof(2), dof(1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	159 otherwise
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	160 error('??? Unrecognized distribution type')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	161 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	162 n2 = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	163 n1 = shp*n1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	164 % calculate empirical distribution for second input dataset
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	165 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	166 [eCD2, ex2] = utils.math.ecdf(y2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	167 CD2 = interp1(ex2, eCD2, x1, 'linear');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	168 n2 = length(y2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	169 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	170
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	171 KSstatistic = max(abs(CD1 - CD2));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	172
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	173 if isempty(criticalValue)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	174 criticalValue = utils.math.SKcriticalvalues(n1, n2, alpha/2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	175 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	176
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	177 % "H = 0" implies that we "Do not reject the null hypothesis at the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	178 % significance level of alpha," and "H = 1" implies that we "Reject null
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	179 % hypothesis at significance level of alpha."
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	180 H = (KSstatistic > criticalValue);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	181
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	182 if nargout > 3
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	183 pValue = utils.math.KSpValue(KSstatistic, n1, n2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	184 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	185
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	186 end

0

f0afece42f48 Import.