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
University Maths Notes: Probability and Statistics – The Lognormal Distribution
A non – negative random variableis
said to have a lognormal distribution if the random variablehas
a normal distribution. The resulting probability density function of
a lognormal random variable whenis
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
