Computes the Lognormal PDF.
p = nisp_lognormalpdf ( x ) p = nisp_lognormalpdf ( x , mu ) p = nisp_lognormalpdf ( x , mu , sigma )
a matrix of doubles
a matrix of doubles, the mean of the underlying normal variable (default mu = 0).
a matrix of doubles, the variance of the underlying normal variable (default sigma = 1).
a matrix of doubles, the probability
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
for x > 0, and f(x)=0 if not.
TODO : improve implementation (check inf, nan, etc...)
// See Dider Pelat, "Bases et méthodes pour le traitement de données" scf(); x = linspace ( 0 , 5 , 1000 ); p = nisp_lognormalpdf ( x , 0.0 , 1.0 ); plot ( x , p ); xtitle("The log-normale probability distribution function","X","P(x)"); // See http://en.wikipedia.org/wiki/File:Lognormal_distribution_PDF.png scf(); x = linspace ( 0 , 5 , 1000 ); p = nisp_lognormalpdf ( x , 0.0 , 10 ); plot ( x , p , "k" ); p = nisp_lognormalpdf ( x , 0.0 , 3/2 ); plot ( x , p , "b" ); p = nisp_lognormalpdf ( x , 0.0 , 1 ); plot ( x , p , "g" ); p = nisp_lognormalpdf ( x , 0.0 , 1/2 ); plot ( x , p , "y" ); p = nisp_lognormalpdf ( x , 0.0 , 1/4 ); plot ( x , p , "r" ); legend ( ["s=10" "s=3/2" "s=1" "s=1/2" "s=1/4"] ); xtitle("The log-normale probability distribution function","X","P(x)");
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