The Lognormal Distribution
A non – negative random variable
is said to have a lognormal distribution if the random variable
has a normal distribution. The resulting probability density function of a lognormal random variable when
is normally distributed with parameters
and
is
It must be noted thatandare not the mean and standard deviation ofbut of
The mean and variance ofare
and
Becausehas a normal distribution the cumulative distribution function ofcan be expressed in terms of the cumulative distribution function of the standard normal random variable
Example: If
and
then
