On the Tails of the Distribution of the Sum of Lognormals

—Finding the distribution of the sum of lognormal We assume in this paper that the terms Yi are independent. The random variables is an important mathematical problem in probability density function (pdf) of each term is lognormal: wireless communications, as well as in many other fields. While several methods exist to approximate this distribution, their performance tends to deteriorate in both tails. Finding a good ( ) overall fit remains an open problem. Other disadvantages of these methods are their complexity and, in some cases, their limitation to particular scenarios. In this paper we examine the sum of independent lognormal random variables with arbitrary parameters. We define the concept of best lognormal fit to a tail and show what it means in terms of convergence. We restate a known result about asymptotes to the higher tail of the distribution. To our knowledge, the lower tail has not yet been studied. We give a simple closed-form expression for an asymptote to the lower ...

• Type: Conference
• Year: 2007
• Where: ICC
• Authors: Sebastien S. Szyszkowicz, Halim Yanikomeroglu
• Keywords: Communications, ICC 2007, Important Mathematical Problem, Lower Tail, Random Variables