SoLN paper supporting materials
Supporting Materials for Keelin, et. al. (2019)
This page contains supporting materials for the paper
- Thomas W. Keelin, Lonnie Chrisman, Sam L. Savage (2019), "Extremely accurate sums of Lognormals in closed form using Metalog distributions", submitted to the Proceedings of the 2019 Winter Simulation Conference.
This paper has been submitted. Until final copy is complete, this page and the downloadable materials may be revised.
We provide closed-form equations that closely approximate the sum of iid lognormal distributions as a function of lognormal parameters, μ and σ, and of N, the finite number of such distributions to be summed. This is accomplished through a finite table of inputs to a metalog distribution for a limited set of lognormal shape parameters and N’s, which may then be interpolated to estimate the continuous set of lognormal parameters and countable N’s. Uses include estimating total impact of N risk events, each with iid individual lognormal impact, noise in wireless communications networks and other applications. Furthermore, beyond lognormals, the approach may be directly applied to sums of iid variables from virtually any continuous distribution.
Our algorithm computes CDF, Inverse CDF, and probability densities for an Average (or sum) of N Log Normal distributions to a maximum error in CDF of less that 0.01 for all N from 2 to 100 and σ from 0.04 to 1.5. We are providing the following Analytica implementation of the algorithm for download:
- Download: Sum of LogNormal Library.ana
If you want to implement this in a different language, we note that it is almost trivial to implement (assuming you have a matrix multiply routine) once you have the Q-tables. See the paper for the details.
The algorithm uses pre-compiled Q-tables. The Sum of LogNormal Library.ana includes these table, or you can download just the tables here as an Excel spreadsheet.
- Download: Sum of LogNormal Q-tables.xlsx