New characterizations of the (discrete) Lindley distribution and their applications
Publication date
2023-05-10
Document type
Forschungsartikel
Author
Wang, Shaochen
Organisational unit
ISSN
Series or journal
Mathematics and computers in simulation
Periodical volume
212
First page
310
Last page
322
Peer-reviewed
✅
Part of the university bibliography
✅
Keyword
Lindley distribution
Distributional characterizations
Stein characterizations
Carleman’s condition
Moment estimation
Goodness-of-fit tests
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.
Version
Published version
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