A Novel Discrete Distribution Based on the Mixture of Poisson and Sum of Two Lindley Random Variables

Accepted - September 2023

Abstract

The distribution of the sum of two independent Lindley random variables having the same parameter defines the 2S-Lindley distribution recently introduced in the statistical literature. In this paper, we use it to create a new one-parameter discrete compound distribution called the Poisson 2S-Lindley distribution. 

The mathematical and statistical properties of the proposed distribution are investigated and analyzed systematically. Subsequently, a statistical standpoint is adopted. Various estimation methods are considered, and an extensive simulation study is conducted to compare them. A count regression model as well as a first-order integer-valued autoregressive process based on the proposed model are constructed. In total, four real data sets in different fields are used to prove the empirical importance of the distribution.