Two Families of Continuous Probability Distributions Generated by the Discrete Lindley Distribution

Srdjan Kadić (), Božidar V. Popović and Ali İ. Genç
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Srdjan Kadić: Faculty of Science and Mathematics, University of Montenegro, 81000 Podgorica, Montenegro
Božidar V. Popović: Faculty of Science and Mathematics, University of Montenegro, 81000 Podgorica, Montenegro
Ali İ. Genç: Department of Statistics, Cukurova University, 01290 Adana, Turkey

Mathematics, 2023, vol. 11, issue 2, 1-22

Abstract: In this paper, we construct two new families of distributions generated by the discrete Lindley distribution. Some mathematical properties of the new families are derived. Some special distributions from these families can be constructed by choosing some baseline distributions, such as exponential, Pareto and standard logistic distributions. We study in detail the properties of the two models resulting from the exponential baseline, among others. These two models have different shape characteristics. The model parameters are estimated by maximum likelihood, and related algorithms are proposed for the computation of the estimates. The existence of the maximum-likelihood estimators is discussed. Two applications prove its usefulness in real data fitting.

Keywords: discrete lindley distribution; EM algorithm; existence of the maximum likelihood estimate; moments (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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