I am trying to calculate the sum of two or more lognormal distributions represented by mean and standard deviation. However, I didn't find any literature that clearly mentions such a formula.
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1Can I please confirm that you want to examine the distribution of the sum of two or more lognormal random variables (since distribution functions are not usually summed)? Also, do all of these random variables have the same mean and standard deviation, or do they have different means and standard deviations? – Ben Mar 23 '23 at 04:58
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If you're trying to find the probability distribution function of A + B, where A ~ lognormal(μ₁, σ₁) and B ~ lognormal(μ₂, σ₂), I don't think a closed form solution exists (Dufresne, Daniel. "Sums of lognormals." Actuarial Research Conference, 2008). Papers by Wu (DOI: 10.1109/GLOCOM.2005.1578407) and Lo (DOI: 10.1155/2012/838397) offer closed form approximations and discuss other options.
