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wlognpdf

PURPOSE

Lognormal probability density function

SYNOPSIS

f = wlognpdf(x,m,v);

DESCRIPTION

``` WLOGNPDF Lognormal probability density function

CALL:  f = wlognpdf(x,m,s);

f = density function evaluated at x
m = mean of log(x)     (default 0)
v = variance of log(x) (default 1)

The Lognormal distribution is defined by its pdf

f(x) = exp(-(log(x)-m)^2/(2*v))/sqrt(v*2*pi*x^2), x>=0.

Example:
x = linspace(0,3,200);
p1 = wlognpdf(x,0,1); p2 = wlognpdf(x,.5,0.25);
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:
 dist2dfun is an internal function to dist2dcdf dist2dprb. dist2dpdf Joint 2D PDF computed as f(x1|X2=x2)*f(x2) ltwcpdf Long Term Wave Climate PDF of significant wave height and wave period mdist2dpdf Joint 2D PDF due to Plackett given as f{x1}*f{x2}*G(x1,x2;Psi). mk87pdf Myrhaug and Kjeldsen (1987) joint (Scf,Hd) PDF.

SOURCE CODE

```001 function f = wlognpdf(x,m,v);
002 %WLOGNPDF Lognormal probability density function
003 %
004 % CALL:  f = wlognpdf(x,m,s);
005 %
006 %        f = density function evaluated at x
007 %        m = mean of log(x)     (default 0)
008 %        v = variance of log(x) (default 1)
009 %
010 % The Lognormal distribution is defined by its pdf
011 %
012 %     f(x) = exp(-(log(x)-m)^2/(2*v))/sqrt(v*2*pi*x^2), x>=0.
013 %
014 % Example:
015 %   x = linspace(0,3,200);
016 %   p1 = wlognpdf(x,0,1); p2 = wlognpdf(x,.5,0.25);
017 %   plot(x,p1,x,p2)
018
019
020 % Reference: Cohen & Whittle, (1988) "Parameter Estimation in Reliability
021 % and Life Span Models", p. 59 ff, Marcel Dekker.
022
023 % Tested on; Matlab 5.3
024 % History:
025 % revised pab 24.10.2000
026 %  - added comnsize, nargchk
027 %  - added default values
028 %  - fixed a bug in the parameterization
030
031 error(nargchk(1,3,nargin))
032 if nargin<2|isempty(m),  m=0;  end
033 if nargin<3|isempty(v),  v=1;  end
034
035 [errorcode, x, m, v] = comnsize (x,m, v);
036 if (errorcode > 0)
037   error ('x, m and v must be of common size or scalar');
038 end
039
040 f=zeros(size(x));
041
042 k = find (x>0&v>0);
043 if any(k)
044   f(k)=1./sqrt(2*pi*v(k)).*exp(-0.5*(log(x(k))-m(k)).^2./v(k))./x(k);
045 end
046
047 k1 = find (v<=0);
048 if any (k1)
049   tmp=NaN;
050   f(k1) = tmp(ones(size(k1)));
051 end
052
053
054
055
056```

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

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