New characterizations of the (discrete) Lindley distribution and their applications

Shaochen Wang and Christian H. Weiß

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 212, issue C, 310-322

Abstract: A Stein-type characterization of the Lindley distribution is derived. It is shown that if using the generalized derivative in the sense of distributions, one can choose all indicator functions as the characterization functions class. This extends some known recent results about characterizations of the Lindley distribution. In addition, a new characterization based on another independent exponential random variable is also provided. As an application of the novel results, some moment formulas related to the Lindley distribution are obtained. Furthermore, generalized method-of-moments estimators for both the discrete and continuous Lindley distribution are proposed, which lead to a notably lower bias at the cost of an only modest increase in mean squared error compared to existing estimators. It is also demonstrated how the Stein characterization might be used to construct a goodness-of-fit test with respect to the null hypothesis of the Lindley distribution. The paper concludes with an illustrative real-data example.

Keywords: Lindley distribution; Distributional characterizations; Stein characterizations; Carleman’s condition; Moment estimation; Goodness-of-fit tests (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:212:y:2023:i:c:p:310-322

DOI: 10.1016/j.matcom.2023.05.003

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