WGUMBTEST Tests whether the shape parameter in a GEV is equal to zero CALL: p = wgumbtest(x,a) p = p-value in the test x = the sample a = significance level (default a=0.05) The Gumbel distribution (see wgumbcdf) is a GEV distribution (see wgevcdf) with shape parameter k = 0. To test if a given set of data is generated by a Gumbel distribution, a test of the hypothesis k = 0 may be based on the PWM estimator of k. On the null hypothesis k = 0, the estimator is asymptotically distributed as N(0,0.5633/n) (where n is the number of observations). Example: x1 = wgevrnd(0.02,2,7.5,50,1); wgumbtest(x1); x2 = wgevrnd(0.20,2,7.5,50,1); wgumbtest(x2); See also wgumbcdf, wgevcdf
Parameter estimates for GEV data | |
Normal cumulative distribution function | |
Convert number to string. (Fast version) |
001 function p = wgumbtest(x,a) 002 %WGUMBTEST Tests whether the shape parameter in a GEV is equal to zero 003 % 004 % CALL: p = wgumbtest(x,a) 005 % 006 % p = p-value in the test 007 % x = the sample 008 % a = significance level (default a=0.05) 009 % 010 % The Gumbel distribution (see wgumbcdf) is a GEV distribution (see 011 % wgevcdf) with shape parameter k = 0. To test if a given set of data 012 % is generated by a Gumbel distribution, a test of the hypothesis k = 0 013 % may be based on the PWM estimator of k. On the null hypothesis k = 0, 014 % the estimator is asymptotically distributed as N(0,0.5633/n) (where n 015 % is the number of observations). 016 % 017 % Example: 018 % x1 = wgevrnd(0.02,2,7.5,50,1); 019 % wgumbtest(x1); 020 % x2 = wgevrnd(0.20,2,7.5,50,1); 021 % wgumbtest(x2); 022 % 023 % See also wgumbcdf, wgevcdf 024 025 % References 026 % Hosking, J.R.M, Wallis, J.R. and Wood E.F. (1985) 027 % Estimation of the generalized extreme-value distribution by the 028 % method of probability-weighted moments 029 % Technometrics (27), pp. 251-261 030 031 % Tested on; Matlab 5.3 032 % History: 033 % Revised by jr 31.08.1999 034 % revised ms 15.06.2000 035 % - updated header info 036 % - changed name to wgumbtest (from gumbtest) 037 % - added optional significance level 038 % - added w* to used WAFO-files 039 040 if nargin < 2 041 a=.05; 042 end 043 044 [r] = wgevfit(x,'pwm',[],0); 045 046 z = r(1)*(length(x)/0.5633)^0.5; 047 disp(' ') 048 disp(' Null hypothesis: Parent distribution is GEV with k = 0.') 049 disp(' ') 050 p = 1-wnormcdf(abs(z),0,1); 051 if (p>a), 052 disp(' The null hypothesis cannot be rejected.') 053 else 054 disp([' Reject the null hypothesis with p-value p = ',num2str(p)]) 055 if z > 0 056 disp(' in favour of the alternative hypothesis: k > 0.') 057 else 058 disp(' in favour of the alternative hypothesis: k < 0.') 059 end 060 end 061 disp(' ') 062
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