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

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.