Moment of Lognormal distribution
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How do I compute the mth moment of the lognormal distribution?
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Torsten
2023-9-19
编辑:Torsten
2023-9-19
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)
double(subs(moment_k,[k mu sigma],[4 0.2 0.3]))
f1 = x^k/(sqrt(2*sym(pi))*sigma*x)*exp(-(log(x)-mu)^2/(2*sigma^2));
moment1_k = int(f,x,0,Inf)
double(subs(moment1_k,[k mu sigma],[4 0.2 0.3]))
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Bruno Luong
2023-9-19
"All moments of the log-normal distribution exist and"
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1487407/image.png)
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