This paper presents efficient and convenient methods for computing the sum of large number of lognormal (LN) random variables (RVs) while utilizing the unexpanded form for the characteristic function of the sum obtained previously. These methods are (1) the application of appropriate quadrature rules to the integral involving the characteristic function for the sum after a proper change of variables, and (2) the application of the Epsilon algorithm to reduce the number of needed computations. The Epsilon algorithm is also used to compute the distribution for the sum of correlated LN RVs. Results indicate that while (1) presents a simple to evaluate sum in terms of the weights and nodes of the chosen quadrature rule, it may require 100 to 1,000s of terms to arrive at a reasonable approximation of the target cumulative distribution function. The second method reduces the needed evaluations to as little as 10 and improves the accuracy for both the lower end and higher end of the approximated cdf.

Title

Arabian Journal for Science and Engineering

Publisher

Springer Nature, KFUPM

Publisher Country

Saudi Arabia

Indexing

Scopus

Impact Factor

2.0

Publication Type

Both (Printed and Online)

Volume

39

Year

2014

Pages

3953–3961