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wgumbcdf

PURPOSE ^

Gumbel cumulative distribution function.

SYNOPSIS ^

F = wgumbcdf(x,a,b,trunc)

DESCRIPTION ^

 WGUMBCDF Gumbel cumulative distribution function.
 
  CALL:  F = wgumbcdf(x,a,b,trunc) 
    
    F    = Gumbel cdf evaluated at x
   a, b  = parameters of the Gumbel distribution.
   trunc = 0  regular gumbel distribution (default)
           1  truncated gumbel distribution 
 
   Gumbel CDF  is given by :                           
        F(x) = exp(-exp(-(x-b)/a))    -inf < x < inf, a>0
   or the truncated 
        F(x) = [exp(-exp(-(x-b)/a))-exp(-exp(b/a))]/(1-exp(-exp(b/a))) 
            0 < x < inf,  a>0
 
 
  Example: 
    x = linspace(-4,6,200);
    p1 = wgumbcdf(x,2,0); p2 = wgumbcdf(x,1,1);
    plot(x,p1,x,p2)
 
  See also  wgumbfit, wgumbrnd, wgumbpdf, wgumbinv, wgumbstat, wgumbplot

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function F = wgumbcdf(x,a,b,trunc)
002 %WGUMBCDF Gumbel cumulative distribution function.
003 %
004 % CALL:  F = wgumbcdf(x,a,b,trunc) 
005 %   
006 %   F    = Gumbel cdf evaluated at x
007 %  a, b  = parameters of the Gumbel distribution.
008 %  trunc = 0  regular gumbel distribution (default)
009 %          1  truncated gumbel distribution 
010 %
011 %  Gumbel CDF  is given by :                           
012 %       F(x) = exp(-exp(-(x-b)/a))    -inf < x < inf, a>0
013 %  or the truncated 
014 %       F(x) = [exp(-exp(-(x-b)/a))-exp(-exp(b/a))]/(1-exp(-exp(b/a))) 
015 %           0 < x < inf,  a>0
016 %
017 %
018 % Example: 
019 %   x = linspace(-4,6,200);
020 %   p1 = wgumbcdf(x,2,0); p2 = wgumbcdf(x,1,1);
021 %   plot(x,p1,x,p2)
022 %
023 % See also  wgumbfit, wgumbrnd, wgumbpdf, wgumbinv, wgumbstat, wgumbplot
024 
025 
026 
027 %  tested on: matlab 5.2
028 % history
029 % revised pab 8.11.1999
030 % updated header info
031 %   Per A. Brodtkorb 17.10.98
032 % rewritten ms 19.06.2000
033 % revised pab 25.10.2000
034 % - added nargchk+comnsize
035 
036 % Reference: 
037 %  Johnson  N.L., Kotz S. and Balakrishnan, N. (1994)
038 %  Continuous Univariate Distributions, Volume 2. Wiley. 
039 
040 
041 error(nargchk(3,4,nargin))
042 if nargin<4|isempty(trunc), trunc=0;end
043 
044 [errorcode x a b] = comnsize(x,a,b);
045 if errorcode > 0
046     error('x, a and b must be of common size or scalar.');
047 end
048 F=zeros(size(x));
049 k1 = find(a>0);
050 if any(k1),
051   F(k1)=exp(-exp(-(x(k1) -b(k1))./a(k1)) );
052   if trunc,
053     tmp=exp(-exp(b(k1)./a(k1)));
054     F(k1)=(F(k1)-tmp)./(1-tmp).*(x(k1)>0);
055   end
056 end
057 
058 k2=find(a<=0);
059 if any(k2)
060   F(k2)=NaN;
061 end
062 
063 
064 
065

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

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