Name

nisp_lognormalpdf — Computes the Lognormal PDF.

Calling Sequence

   p = nisp_lognormalpdf ( x )
   p = nisp_lognormalpdf ( x , mu )
   p = nisp_lognormalpdf ( 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).

p:

a matrix of doubles, the probability

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

for x > 0, and f(x)=0 if not.

TODO : improve implementation (check inf, nan, etc...)

Examples

// 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)");

   

Authors

Copyright (C) 2008-2011 - INRIA - Michael Baudin

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