Statistical Properties and Different Estimation Procedures of Poisson-Lindley Distribution

In this paper, we propose a new class of distributions by compounding Lindley distributed random variates with the number of variates being zero-truncated Poisson distribution. This model is called a compound zero-truncated Poisson-Lindley distribution with two parameters. Different statistical properties of the proposed model are discussed. We describe different methods of estimation for the unknown parameters involved in the model. These methods include maximum likelihood, least squares, weighted least squares, Cramer-von Mises, maximum product of spacings, Anderson-Darling and right-tail Anderson-Darling methods. Numerical simulation experiments are conducted to assess the performance of the so obtained estimators developed from these methods. Finally, the potentiality of the model is studied using one real data set representing the monthly highest snowfall during February 2018, for a subset of stations in the Global Historical Climatological Network of USA. (C) 2021 The Authors. Published by Atlantis Press B.V.

Automated summary

This paper introduces a compound zero-truncated Poisson-Lindley distribution with two parameters, and discusses its various statistical properties. Different estimation methods for the unknown parameters in the model are described, and numerical simulation experiments are conducted to evaluate the performance of the estimators. The potential of the model is studied using real data on monthly highest snowfall from February 2018.