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wgumbtest

PURPOSE ^

Tests whether the shape parameter in a GEV is equal to zero

SYNOPSIS ^

p = wgumbtest(x,a)

DESCRIPTION ^

 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

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

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

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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