I have a question concerning the lognormal distribution. I want to simulate income using MC simulation. Assume that income is lognormal distributed. I also have some historical data that I use to calculate the standard deviation of income. Together with expected income I calculate I calculate the shape and scale parameters. My first question is whether it is correct to calculate the scale parameter as ln(E(X)) - 0,5 ln(1+ Var(X)/E(X)^2)) and the shape parameter of the distribution as ln(1+Var(X)/E(X)^2) and then take the square root to obtain the sd. By doing this I have the distribution of income in terms of logs. I then do MC simulation by generating random numbers from the probability density function.

Is this a correct approach?. I would appreciate any help.

Best,

Herrald