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Lo 2013 derived the following formula for the approximation of the sum of several correlated lognormal random variables by a lognormal distribution. S+=E[∑iXi]=∑iE[Xi]=∑ieμi+σ2i/2σ2S=1/S2+∑i,jcorijσiσjE[Xi]E[Xj]=1/S2+∑i,jcorijσiσjeμi+σ2i/2eμj+σ2j/2μS=ln(S+)−σ2S/2 where S+ is the expected value of the sum, i.e the sum of the expected values of the terms. μs and σS are lognormal distribution parameters of the sum, μi and σi are the lognormal distribution parameters of the added random variables, and corij is the correlation between two added random variables at log scale, which for time is computed from estimated autocorrelation ρk.
This method is implemented with function estimateSumLognormal
, where the full correlation matrix is specified. For computational efficiency, the correlation length can be specified and correlations further apart will not contribute to the sum.
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