The Metalog Distributions

Sum of Lognormal Metalogs

The sum of N independent, identically distributed (iid) lognormal distributions has no closed form expression. For a range of N, we simulated this sum 50 million times to get the nine points on the CDF illustrated. The 9-term semi-bounded metalog, parameterized by these points, runs through each of them exactly. The resulting metalog CDFs and PDFs are (plotted as averages rather than sums) are shown below. For details, see our paper.

9-term metalog representations of average of N iid lognormal distributions (mu=0, sigma=1)