A non – negative random variableis 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 thatand
are not the mean and standard deviation of
but of
The mean and variance of
are
and
Becausehas a normal distribution the cumulative distribution function of
can be expressed in terms of the cumulative distribution function of the standard normal random variable
Example: Ifand
then