Statistical inference for geometric processes with lognormal distribution

A stochastic process {X-i, i = 1, 2,...} is a geometric process if there exists a>0 such that {a(i-1)X(i), i = 1,2,...} generates a renewal process. In this paper, under the assumption that X-1 follows a lognormal distribution, we study the statistical inference problem for the geometric process. The parameters a,lambda, and sigma(2), where lambda and sigma(2) are, respectively, the mean and variance of X-1, are estimated by the maximum likelihood method and a modified moment method. Then some suggestions are made based on the theoretical results, the simulation experiments, and the real data analysis. (C) 1998 Elsevier Science B.V. All rights reserved.