distfun_lognpdf

Calling Sequence

y = distfun_lognpdf ( x )
y = distfun_lognpdf ( x , mu )
y = distfun_lognpdf ( x , mu , sigma )

Parameters

x:: a matrix of doubles
mu:: a matrix of doubles, the mean of the underlying normal variable (default mu = 0).
sigma:: a matrix of doubles, the variance of the underlying normal variable (default sigma = 1).
y:: a matrix of doubles, the density

Description

This function computes the Lognormal PDF.

Any scalar input argument is expanded to a matrix of doubles of the same size as the other input arguments.

Any optional input argument equal to the empty matrix will be set to its default value.

The Lognormal distribution with parameters mu and sigma has density

Examples

// See Dider Pelat
// "Bases et méthodes pour le traitement de données"
scf();
x = linspace ( 0 , 5 , 1000 );
y = distfun_lognpdf ( x , 0.0 , 1.0 );
plot ( x , y );
xtitle("The log-normale PDF","x","f");

// See wikipedia

// Examples from wikipedia
scf();
x = linspace ( 0 , 5 , 1000 );
y = distfun_lognpdf ( x , 0.0 , 10 );
plot ( x , y , "k" );
y = distfun_lognpdf ( x , 0.0 , 3/2 );
plot ( x , y , "b" );
y = distfun_lognpdf ( x , 0.0 , 1 );
plot ( x , y , "g" );
y = distfun_lognpdf ( x , 0.0 , 1/2 );
plot ( x , y , "y" );
y = distfun_lognpdf ( x , 0.0 , 1/4 );
plot ( x , y , "r" );
legend ( ["s=10" "s=3/2" "s=1" "s=1/2" "s=1/4"] );
xtitle("The log-normale PDF","X","f(X)");

Authors

Bibliography

Dider Pelat, "Bases et méthodes pour le traitement de données", section 8.2.8, "Loi log-normale".

Wikipedia, Lognormal probability distribution function, http://en.wikipedia.org/wiki/File:Lognormal_distribution_PDF.png

Wikipedia, Lognormal cumulated distribution function, http://en.wikipedia.org/wiki/File:Lognormal_distribution_CDF.png