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# wbetapdf

## PURPOSE

Beta probability density function

## SYNOPSIS

f = wbetapdf(x,a,b)

## DESCRIPTION

 WBETAPDF   Beta probability density function

CALL:  f = wbetapdf(x,a,b);

f = density function evaluated at x
x   = matrix
a, b = distribution parameters

The PDF is defined by:

f = x^(a-1)*(1-x)^(b-1)/H(a,b)    0<= x <= 1, a>0, b>0

where H(a,b) is a normalization constant.
Example:
x = linspace(0,1,200);
p1 = wbetapdf(x,1,1); p2 = wbetapdf(x,2,2);
plot(x,p1,x,p2)

## CROSS-REFERENCE INFORMATION

This function calls:
 comnsize Check if all input arguments are either scalar or of common size. beta Beta function. error Display message and abort function. nan Not-a-Number.
This function is called by:
 braylpdf Beta Rayleigh PDF of wave heigth wbetainv Inverse of the Beta distribution function wfpdf Snedecor's F probability density function

## SOURCE CODE

001 function f = wbetapdf(x,a,b)
002 %WBETAPDF   Beta probability density function
003 %
004 % CALL:  f = wbetapdf(x,a,b);
005 %
006 %    f = density function evaluated at x
007 %  x   = matrix
008 % a, b = distribution parameters
009 %
010 %  The PDF is defined by:
011 %
012 %   f = x^(a-1)*(1-x)^(b-1)/H(a,b)    0<= x <= 1, a>0, b>0
013 %
014 % where H(a,b) is a normalization constant.
015 % Example:
016 %   x = linspace(0,1,200);
017 %   p1 = wbetapdf(x,1,1); p2 = wbetapdf(x,2,2);
018 %   plot(x,p1,x,p2)
019
020
021 % tested on matlab 5.3
022 %History:
023 %revised pab 29.10.2000
026 %       Anders Holtsberg, 18-11-93
027 %       Copyright (c) Anders Holtsberg
028
029
030
031
032 error(nargchk(3,3,nargin))
033 [errorcode x,a,b] = comnsize(x,a,b);
034 if errorcode>0,
035   error('x, a and b must be of common size or scalar');
036 end
037
038 f = zeros(size(x));
039
040 ok = (a>0 & b>0);
041
042 k = find(x>=0&x<=1 & ok);
043 if any(k)
044   f(k) = x(k).^(a(k)-1) .* (1-x(k)).^(b(k)-1) ./ beta(a(k),b(k));
045 end
046
047
048
049
050 k=find(~ok);
051 if (any(k)),
052   F(k)=NaN;
053 end
054

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

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