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Distfun >> Distfun > LogNormal > distfun_logncdf

distfun_logncdf

Lognormal CDF

Calling Sequence

p = distfun_logncdf ( x , mu , sigma )
p = distfun_logncdf ( x , mu , sigma , lowertail )

Parameters

x:

a matrix of doubles

mu:

a matrix of doubles, the mean of the underlying normal variable.

sigma:

a matrix of doubles, the variance of the underlying normal variable. sigma>0.

lowertail :

a 1-by-1 matrix of booleans, the tail (default lowertail=%t). If lowertail is true (the default), then considers P(X<=x) otherwise P(X>x).

p:

a matrix of doubles, the probability

Description

This function computes the Lognormal Cumulated Density Function.

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.

Examples

p = distfun_logncdf ( 2. , 3. , 10. )
pexpected = 0.4087797

// See wikipedia.org
scf();
x = linspace ( 0 , 3 , 1000 );
p = distfun_logncdf ( x , 0. , 10 );
plot ( x , p , "k" );
p = distfun_logncdf ( x , 0. , 3/2 );
plot ( x , p , "b" );
p = distfun_logncdf ( x , 0. , 1 );
plot ( x , p , "g" );
p = distfun_logncdf ( x , 0. , 1/2 );
plot ( x , p , "y" );
p = distfun_logncdf ( x , 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 CDF","x","$P(X\leq x)$");

// See upper tail : 2.0301530180231740447e-14
p = distfun_logncdf ( 1.e7 , 1. , 2. , %f )

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


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