WGUMBSTAT Mean and variance for the Gumbel distribution. CALL: [m,v] = wgumbstat(a,b,trunc) m, v = the mean and variance, respectively a, b = parameters of the Gumbel distribution (see wgumbcdf) trunc = 0 regular gumbel distribution (default) 1 truncated gumbel distribution (not available) Mean (m) and variance (v) for the Gumbel distribution is m=Euler*a+b and v=(a*pi)^2/6 where Euler is Euler's constant 0.5772... Example: X = wgumbrnd(5,10,[],1000,1); [mean(X) var(X)] % Estimated mean and variance [m,v] = wgumbstat(5,10) % True mean and variance See also gumbfit, gumbpdf, gumbcdf, gumbinv, gumbpdf
Check if all input arguments are either scalar or of common size. | |
Display message and abort function. | |
Not-a-Number. |
Joint 2D CDF computed as int F(X1 | |
Mean and variance for the DIST2D distribution | |
Mean and variance for the MDIST2D distribution. |
001 function [m,v]= wgumbstat(a,b,trunc); 002 %WGUMBSTAT Mean and variance for the Gumbel distribution. 003 % 004 % CALL: [m,v] = wgumbstat(a,b,trunc) 005 % 006 % m, v = the mean and variance, respectively 007 % a, b = parameters of the Gumbel distribution (see wgumbcdf) 008 % trunc = 0 regular gumbel distribution (default) 009 % 1 truncated gumbel distribution (not available) 010 % 011 % Mean (m) and variance (v) for the Gumbel distribution is 012 % 013 % m=Euler*a+b and v=(a*pi)^2/6 where Euler is Euler's 014 % constant 0.5772... 015 % 016 % Example: 017 % X = wgumbrnd(5,10,[],1000,1); 018 % [mean(X) var(X)] % Estimated mean and variance 019 % [m,v] = wgumbstat(5,10) % True mean and variance 020 % 021 % See also gumbfit, gumbpdf, gumbcdf, gumbinv, gumbpdf 022 023 % Reference: 024 % Johnson N.L., Kotz S. and Balakrishnan, N. (1994) 025 % Continuous Univariate Distributions, Volume 2. Wiley. 026 027 028 % tested on: matlab 5.2 029 % history 030 % revised pab 8.11.1999 031 % updated header info 032 % Per A. Brodtkorb 17.10.98 033 % revised ms 14.06.2000 034 % - changed name to wgumbstat (from gumbstat) 035 % - revised header info 036 % - noted that calculations are wrong for trunc=1 (not corrected) 037 038 error(nargchk(2,3,nargin)) 039 040 [errorcode a b] = comnsize(a,b); 041 if errorcode > 0, 042 error('a and b must be of common size or scalar.'); 043 end 044 if nargin < 3 | isempty(trunc), 045 trunc=0; % default value is not truncated 046 end 047 048 049 m = 0.5772*a+b; %mean 050 v = pi^2/6*a.^2; %variance 051 052 if trunc, %This is not correct (ms) 053 tmp=1-exp(-exp( b./a)); 054 m=m./tmp; 055 v=v./tmp; 056 end 057 % Return NaN if A is negative or zero. 058 k = find(a <= 0); 059 if any(k) 060 tmp = NaN; 061 m(k) = tmp(ones(size(k))); 062 v(k) = m(k); 063 end 064 065
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