On the approximation of sum of lognormal for correlated variates and implementation
Asyraf Nadia Mohd Yunus, Nora Muda, Abdul Rahman Othman, Sonia Aïssa
TL;DR
This paper compares three methods for approximating the sum of correlated lognormal variables and finds that the Wilkinson method performs best across various scenarios.
Contribution
The study provides new empirical evidence that the Wilkinson method outperforms others for correlated lognormal sums.
Findings
Wilkinson approximation has the lowest Type I error rates across all tested correlation structures and sample sizes.
Results were validated using real-world datasets from engineering and finance, confirming Wilkinson's superior performance.
The findings contradict prior telecommunications literature that favored the Schwartz & Yeh method.
Abstract
In probabilistic modeling across engineering, finance, and telecommunications, sums of lognormal random variables frequently occur, yet no closed-form expression exists for their distribution. This study systematically evaluates three approximation methods—Wilkinson (W), Schwartz & Yeh (SY), and Inverse (I)—for correlated lognormal variates across varying sample sizes and correlation structures. Using Monte Carlo simulations with 5, 15, 25, and 30 samples and correlation coefficients of 0.3, 0.6, and 0.9, we compared Type I error rates through Anderson-Darling goodness-of-fit tests. Our findings demonstrate that the Wilkinson approximation consistently outperforms the other methods for correlated variates, exhibiting the lowest Type I error rates across all tested scenarios. This contradicts some previous findings in telecommunications literature where SY was preferred. We validated…
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Taxonomy
TopicsImage and Signal Denoising Methods