Moment of Lognormal distribution

How do I compute the mth moment of the lognormal distribution?

Answer 1

[Torsten]

https://math.stackexchange.com/questions/628681/how-to-compute-moments-of-log-normal-distribution

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

[Bruno Luong]

If you make variable change

X := exp(x) from f, so dX/dx = X, or dx= DX/X

shouldn't you define then

f1 = x^(k-1) / ....

[Torsten]

There is an additional x in the denominator.

[Bruno Luong]

Oh I miss it.

Answer 2

[Bruno Luong]

https://en.wikipedia.org/wiki/Log-normal_distribution

"All moments of the log-normal distribution exist and"

[Daniel Amankwah]

I actually need the matlab command.

[Bruno Luong]

mu = 0.2;
sigma = 0.3;
n = 4;
Mn = exp(n*mu + (n*sigma)^2/2)

Mn = 4.5722

[Torsten]

:-)