On a Sum and Difference of Two Lindley Distributions

Theory and Application

Abstract

This paper investigates theoretical and practical aspects of two basic random variables constructed from Lindley distribution. The first one is defined as the sum of two independent random variables following the Lindley distribution (with the same parameter) and the second one is defined as the difference of two independent random variables following the Lindley distribution (with the same parameter). Then, statistical inference is performed. In both the cases, we assess the performance of the maximum likelihood estimators using simulation studies. The usefulness of the corresponding models are proved using goodness-of-fit tests based on different real datasets.