A Recursive Exponential-Gamma Mixture: a New Generalized of the Lindley Distribution

TL;DR

This paper introduces a new recursive mixture of Lindley and Gamma distributions that simplifies the model while maintaining flexibility, demonstrating its advantages through statistical properties and real data examples.

Contribution

A novel recursive exponential-Gamma mixture distribution is proposed, offering a simpler yet flexible alternative to existing Lindley generalizations.

Findings

The new distribution has desirable statistical properties.

It outperforms existing Lindley generalizations in real data applications.

The distribution is computationally simpler to use.

Abstract

The Lindley distribution was first introduced by Lindley in 1958 for Bayesian computations. Over the past years, various generalizations of this distribution have been proposed by different authors. The generalized Lindley distributions sometimes have many parameters, and although they show good flexibility, their statistical form becomes complicated. In this article, we propose a new and simple distribution determined by the recursive relation of the Lindley distribution and the Gamma distribution with specific weights. Subsequently, some statistical properties of this distribution are examined, and with real numerical examples, its superiority over the Lindley generalizations is demonstrated.