An error bound for moment matching methods of lognormal sum distributions

Abstract

SUMMARYTo evaluate the distribution function of a sum of lognormal random variables it is common to use approximation methods based on moment matching. These include the classical and simple FentonWilkinson (FW) method, which approximates the sum with a single lognormal variable, having the first two moments matched. In this letter, we give a closed-form bound for the error of the distribution function, resulting from moment matching methods. Numerical evaluation for a typical CDMA case, shows that the bound becomes tight for large processing gains. The error bound can also be used to find bounds on the outage probability.

Limit theorem on the sum of identically distributed equally and positively correlated joint lognormals

“…We support this by some Monte Carlo simulations with large. It should be noted that there exist only a few papers that give purely closed-form results on the SLN problem [1], [2], [7], [9] and [8] and references therein, and only [9] considers correlated terms. The asymptotic behaviour for large appears not to have been studied before.…”

Risk aggregation in Solvency II through recursive log-normals

“…Such moment matching goes back to Wilkinson (1934), and is in communication theory known as the Fenton-Wilkinson approach after Fenton (1960). There is an error bound in Berggren (2005). The early contributions dealt with independent variables only, but extensions to correlated ones can be found in Dufresne (2004) and Henriksen (2008) with efficient Monte Carlo for the extreme tails in Asmussen, Blanchet, Juneja and Rojas-Nandyapa (2011) and a limit theorem in Beaulieu (2012).…”

Network Equilibrium under Cumulative Prospect Theory and Endogenous Stochastic Demand and Supply

“…Following Fenton (1960), X can be approximated by the multivariate lognormal distribution; error bounds for such an approximation are provided by Berggren (2005 …”