WGEVRND Random matrices from a Generalized Extreme Value distribution CALL: R = wgevrnd(k,s,m0,sz) R = matrix of random numbers k = shape parameter in the GEV s = scale parameter in the GEV, s>0 (default 1) m0 = location parameter in the GEV (default 0) sz = size(R) (Default common size of k,s and m0) sz can be a comma separated list or a vector giving the size of R (see zeros for options). The generalized extreme-value distribution is defined by its cdf exp( - (1 - k(x-m)/s))^1/k) ), k~=0 F(x;k,s,m) = exp( -exp(-(x-m)/s) ), k==0 for x>s/k+m (when k<=0) and x<m+s/k (when k>0). The random numbers are generated by the inverse method. Example: R1=wgevrnd(0.5,5,0,1,100); % Finite end-point (R1<4) plot(R1,'.') R2=wgevrnd(0,2,0,1,100); % Gumbel plot(R2,'.') R3=wgevrnd(-.5,.2,0,1,100); % Heavy tailed plot(R3,'.') See also wgevinv, zeros
Check if all input arguments are either scalar or of common size. | |
Inverse of the Generalized Extreme Value distribution function | |
Display message and abort function. |
% CHAPTER5 contains the commands used in Chapter 5 of the tutorial |
001 function r = wgevrnd(k,s,m0,varargin); 002 %WGEVRND Random matrices from a Generalized Extreme Value distribution 003 % 004 % CALL: R = wgevrnd(k,s,m0,sz) 005 % 006 % R = matrix of random numbers 007 % k = shape parameter in the GEV 008 % s = scale parameter in the GEV, s>0 (default 1) 009 % m0 = location parameter in the GEV (default 0) 010 % sz = size(R) (Default common size of k,s and m0) 011 % sz can be a comma separated list or a vector 012 % giving the size of R (see zeros for options). 013 % 014 % The generalized extreme-value distribution is defined by its cdf 015 % 016 % exp( - (1 - k(x-m)/s))^1/k) ), k~=0 017 % F(x;k,s,m) = 018 % exp( -exp(-(x-m)/s) ), k==0 019 % 020 % for x>s/k+m (when k<=0) and x<m+s/k (when k>0). 021 % 022 % The random numbers are generated by the inverse method. 023 % 024 % Example: 025 % R1=wgevrnd(0.5,5,0,1,100); % Finite end-point (R1<4) 026 % plot(R1,'.') 027 % R2=wgevrnd(0,2,0,1,100); % Gumbel 028 % plot(R2,'.') 029 % R3=wgevrnd(-.5,.2,0,1,100); % Heavy tailed 030 % plot(R3,'.') 031 % 032 % See also wgevinv, zeros 033 034 035 % Tested on: Matlab 5.3 036 % History: 037 % Revised by jr 22.12.1999 038 % revised ms 14.06.2000 039 % - updated header info 040 % - changed name to wgevrnd (from gevrnd) 041 % - allowed 3 arguments 042 % revised pab 23.10.2000 043 % - added default s,m0 044 % - added comnsize, nargchk 045 % - added greater flexibility on the sizing of R 046 047 error(nargchk(2,inf,nargin)) 048 if nargin<2|isempty(s), s=1;end 049 if nargin<3|isempty(m0), m0=0;end 050 051 if nargin<4, 052 [errorcode k ,s,m0] = comnsize(k,s,m0); 053 else 054 [errorcode k,s,m0] = comnsize(k,s,m0,zeros(varargin{:})); 055 end 056 if errorcode > 0 057 error('k,s and m0 must be of common size or scalar.'); 058 end 059 060 r = wgevinv(rand(size(k)),k,s,m0); 061 062
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