Q4) How do we model the distribution of a variable whose logarithm is normally distributed?
Lognormal
The lognormal distribution models a variable whose logarithm follows a normal distribution. If ( X ) is lognormally distributed, then ( Y = \ln(X) ) is normally distributed. Parameters are:
- ( \mu ) and ( \sigma^2 ) which are the mean and variance of the variable’s natural logarithm.
- Expected value (mean) = ( e^{\mu + \frac{\sigma^2}{2}} )
- Variance = ( (e^{\sigma^2} - 1)e^{2\mu+\sigma^2} )