Lognormal CDF
p = distfun_logncdf ( x , mu , sigma ) p = distfun_logncdf ( x , mu , sigma , lowertail )
a matrix of doubles
a matrix of doubles, the mean of the underlying normal variable.
a matrix of doubles, the variance of the underlying normal variable. sigma>0.
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).
a matrix of doubles, the probability
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.
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 ) | ![]() | ![]() |
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