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# wtweibpdf

## PURPOSE

Truncated Weibull probability density function

## SYNOPSIS

f = wtweibpdf(x,a,b,c)

## DESCRIPTION

``` WTWEIBPDF Truncated Weibull probability density function

CALL:  f = wtweibpdf(x,a,b,c);

f = density function evaluated at x
a,b,c = parameters

The Weibull distribution is defined by its cdf

F(x;a,c) = 1 -  exp(-((x+c)/a)^b+abs(c/a)^b), x>=0

Some references refer to the Weibull distribution with
a single parameter, this corresponds to WTWEIBPDF with a = 1.

Example:
x = linspace(0,6,200);
p1 = wtweibpdf(x,1,1,2); p2 = wtweibpdf(x,2,2,3);
plot(x,p1,x,p2)```

## CROSS-REFERENCE INFORMATION

This function calls:
 comnsize Check if all input arguments are either scalar or of common size. error Display message and abort function. nan Not-a-Number.
This function is called by:
 dist2dpdf Joint 2D PDF computed as f(x1|X2=x2)*f(x2) jhsnlpdf Joint (Scf,Hd) PDF for nonlinear waves with a JONSWAP spectra. jhspdf Joint (Scf,Hd) PDF for linear waves with JONSWAP spectra. jhvnlpdf Joint (Vcf,Hd) PDF for linear waves with a JONSWAP spectrum. jhvpdf Joint (Vcf,Hd) PDF for linear waves with a JONSWAP spectrum. thpdf Marginal wave height, Hd, PDF for Torsethaugen spectra. thsnlpdf Joint (Scf,Hd) PDF for nonlinear waves with Torsethaugen spectra. thspdf Joint (Scf,Hd) PDF for linear waves with Torsethaugen spectra. thspdf2 Joint (Scf,Hd) PDF for linear waves with Torsethaugen spectra. thsspdf Joint (Scf,Hd) PDF for linear waves in space with Torsethaugen spectra. thvpdf Joint (Vcf,Hd) PDF for linear waves with Torsethaugen spectra.

## SOURCE CODE

```001 function f = wtweibpdf(x,a,b,c)
002 %WTWEIBPDF Truncated Weibull probability density function
003 %
004 % CALL:  f = wtweibpdf(x,a,b,c);
005 %
006 %        f = density function evaluated at x
007 %    a,b,c = parameters
008 %
009 %
010 % The Weibull distribution is defined by its cdf
011 %
012 %  F(x;a,c) = 1 -  exp(-((x+c)/a)^b+abs(c/a)^b), x>=0
013 %
014 %   Some references refer to the Weibull distribution with
015 %   a single parameter, this corresponds to WTWEIBPDF with a = 1.
016 %
017 % Example:
018 %   x = linspace(0,6,200);
019 %   p1 = wtweibpdf(x,1,1,2); p2 = wtweibpdf(x,2,2,3);
020 %   plot(x,p1,x,p2)
021
022 % Reference: Cohen & Whittle, (1988) "Parameter Estimation in Reliability
023 % and Life Span Models", p. 25 ff, Marcel Dekker.
024
025
026 % Tested on; Matlab 5.3
027 % History:
028 % revised pab 12.11.2000
029 %  - added check on f(k): Replace NaN's with zero
030 % revised pab 24.10.2000
031 %  - added comnsize, nargchk
032 % rewritten ms 15.06.2000
033
034
035 error(nargchk(3,4,nargin))
036 if nargin<4|isempty(c),c=0;end
037 [errorcode, x, a,b, c] = comnsize (x,a,b, abs(c));
038 if (errorcode > 0)
039   error ('x, a, b and c must be of common size or scalar');
040 end
041
042 f=zeros(size(x));
043
044 ok = ((b > 0)  & (a > 0));
045
046 k = find (x>=0&ok);
047 if any (k)
048   f(k)=((x(k)+c(k))./a(k)).^(b(k)-1).*b(k)./a(k).*exp(-((x(k)+c(k))./a(k)).^b(k)+abs(c(k)./a(k)).^b(k));
049   k0 = find(isnan(f(k)));
050   if any(k0),
051     f(k(k0))=0;
052   end
053 end
054
055 k1 = find (~ok);
056 if any (k1)
057   tmp=NaN;
058   f(k1) = tmp(ones(size(k1)));
059 end
060
061
062
063
064
065
066```

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

Comments or corrections to the WAFO group

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