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# wtraylpdf

## PURPOSE

Truncated Rayleigh probability density function

## SYNOPSIS

f = wraylpdf(x,b,c);

## DESCRIPTION

``` WTRAYLPDF Truncated Rayleigh probability density function

CALL:  f = wtraylpdf(x,b,c);

f = density function evaluated at x
b = scale parameter
c = truncation parameter (default 0)

The Truncated Rayleigh distribution is defined by its cdf

F(x;b,c) = 1 - exp(-(x-c)^2/(2b^2)+c^2/(2*b^2)), x>=0, b>0

Example:
x = linspace(0,4,200);
p1 = wtraylpdf(x,1); p2 = wtraylpdf(x,0.5,-2);
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)

## SOURCE CODE

```001 function f = wraylpdf(x,b,c);
002 %WTRAYLPDF Truncated Rayleigh probability density function
003 %
004 % CALL:  f = wtraylpdf(x,b,c);
005 %
006 %        f = density function evaluated at x
007 %        b = scale parameter
008 %        c = truncation parameter (default 0)
009 %
010 % The Truncated Rayleigh distribution is defined by its cdf
011 %
012 %  F(x;b,c) = 1 - exp(-(x-c)^2/(2b^2)+c^2/(2*b^2)), x>=0, b>0
013 %
014 % Example:
015 %   x = linspace(0,4,200);
016 %   p1 = wtraylpdf(x,1); p2 = wtraylpdf(x,0.5,-2);
017 %   plot(x,p1,x,p2)
018
019 % Reference: Cohen & Whittle, (1988) "Parameter Estimation in Reliability
020 % and Life Span Models", p. 181 ff, Marcel Dekker.
021
022
023 % Tested on; Matlab 5.3
024 % History:
025 % revised pab 24.10.2000
026 %  - added comnsize, nargchk
028
029
030 error(nargchk(2,3,nargin))
031 if nargin<3|isempty(c),c=0;end
032 [errorcode, x, b,c] = comnsize (x,b,c);
033 if (errorcode > 0)
034   error ('x, b and c must be of common size or scalar');
035 end
036
037 f=zeros(size(x));
038
039 k = find ((x>=0)&(b>0));
040 if any (k)
041   f(k)=(x(k)-c(k)).*exp(-((x(k)-c(k)).^2 -abs(c(k)).^2)./(2*b(k).^2))./b(k).^2;
042 end
043
044 k1 = find (b<=0);
045 if any (k1)
046   tmp=NaN;
047   f(k1) = tmp(ones(size(k1)));
048 end
049
050```

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

Comments or corrections to the WAFO group

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