# How to obtain moment generating function for lognormal distribution.

• May 12th 2009, 10:50 PM
bob000
How to obtain moment generating function for lognormal distribution.
I can obtain
$
M_{X}(t) = e^{\mu t + \sigma^{2}t^{2}/2}
$

as the moment generating function of the normal distribution but I dont see the step to obtain
$
E(X^n) = e^{n \mu + \frac{1}{2}n^{2}\sigma^{2}}
$

as the Taylor series elements of the lognormal moment generating function.
• May 12th 2009, 11:50 PM
matheagle
Since $Y=\ln X$ we have $e^Y=X$.

So, $MGF_Y(t)=E(e^{Yt})=E(X^t)$ using $e^{Yt}=(e^Y)^t=X^t$.

Or $MGF_Y(n)=E(X^n)$.