# Moment of Lognormal distribution

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Daniel Amankwah on 19 Sep 2023
Edited: Torsten on 19 Sep 2023
How do I compute the mth moment of the lognormal distribution?

Torsten on 19 Sep 2023
Edited: Torsten on 19 Sep 2023
or with MATLAB (the second result looks wrong to me):
syms x mu real
syms sigma real positive
syms k integer positive
f = exp(k*x)/(sqrt(2*sym(pi))*sigma)*exp(-(x-mu)^2/(2*sigma^2));
moment_k = int(f,x,-Inf,Inf)
moment_k =
double(subs(moment_k,[k mu sigma],[4 0.2 0.3]))
ans = 4.5722
f1 = x^k/(sqrt(2*sym(pi))*sigma*x)*exp(-(log(x)-mu)^2/(2*sigma^2));
moment1_k = int(f,x,0,Inf)
moment1_k =
double(subs(moment1_k,[k mu sigma],[4 0.2 0.3]))
ans = 4.4306
##### 3 CommentsShow 1 older commentHide 1 older comment
Torsten on 19 Sep 2023
There is an additional x in the denominator.
Bruno Luong on 19 Sep 2023
Oh I miss it.

Bruno Luong on 19 Sep 2023
"All moments of the log-normal distribution exist and"
##### 3 CommentsShow 1 older commentHide 1 older comment
Bruno Luong on 19 Sep 2023
mu = 0.2;
sigma = 0.3;
n = 4;
Mn = exp(n*mu + (n*sigma)^2/2)
Mn = 4.5722
Torsten on 19 Sep 2023
:-)

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