Geometric log-Lindley distribution as an alternative to the Poisson model with application to insurance data

Document Type : Original Scientific Paper

Author

Deprtment of Statistics‎, ‎University of Hormozgan‎, ‎BandarAbbas‎, ‎Iran

Abstract

Mixed discrete distributions are primarily used for modeling over-dispersed count data. The construction of mixed models, such as the mixed Poisson model, is based on the assumption that the distribution parameter of interest is a random variable that follows a specified distribution. In this framework, the marginal distribution of a discrete random variable forms a mixed distribution. This paper introduces a novel discrete distribution derived from the geometric distribution, assuming that the model's parameter follows the log-Lindley distribution. This approach is motivated by situations where the parameter of the geometric distribution is not constant across populations, as is often the case in insurance data, where the probability of a claim varies between different portfolios. This distribution is particularly well-suited for modeling over-dispersed discrete data. The statistical properties of the proposed distribution are examined, and the parameters of the resulting model are estimated. To evaluate the accuracy of the estimates, a simulation study is conducted, and the model's performance is demonstrated using real data.

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Journal of Statistical Modelling: Theory and Applications
Volume 6, Issue 1
January 2025
Pages 151-166

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History

  • Receive Date: 14 August 2025
  • Revise Date: 04 December 2025
  • Accept Date: 22 January 2026

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