On a family that unifies the generalized Marshall-Olkin and Poisson-G family of distributions

Laba Handique; Farrukh Jamal; Subrata Chakraborty

doi:https://doi.org/10.59139/stattrans-2025-007

On a family that unifies the generalized Marshall-Olkin and Poisson-G family of distributions

Laba Handique Department of Statistics, Darrang College, Tezpur, Assam-784001, India ORCID:https://orcid.org/0000-0001-9255-2918 , Farrukh Jamal Department of Statistics, The Islamia University, Bahawalpur 63100, Pakistan ORCID:https://orcid.org/0000-0001-6192-9890 , Subrata Chakraborty Department of Statistics, Dibrugarh University, Dibrugarh-786004, India ORCID:https://orcid.org/0000-0002-6405-1486 Statistics in Transition new series, vol. 26, 2025, 1, pages: 117-134 Published online: 10 March 2025 https://doi.org/10.59139/stattrans-2025-007 Citation: Handique L., Jamal F., Chakraborty S., 2025. On a family that unifies the generalized Marshall-Olkin and Poisson-G family of distributions. Statistics in Transition new series, 26(1), pp. 117-134. https://doi.org/10.59139/stattrans-2025-007

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ARTICLE

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ABSTRACT

The aim of the article is to propose a unification of the generalized Marshall-Olkin (GMO) and Poisson-G (P-G) distributions into a new family of distributions. The density and survival function are expressed as infinite mixtures of an exponentiated-P-G family. The quantile function, asymptotes, shapes, stochastic ordering and Rényi entropy are derived. The paper presents a maximum likelihood estimation with large sample properties. A Monte Carlo simulation is used to examine the pattern of the bias and the mean square error of the maximum likelihood estimators. The utility of the proposed family is illustrated through its comparison with some important models and sub models of the family in terms of modeling real data.

KEYWORDS

GMO family, Poisson-G family, stochastic ordering, MLE, AIC

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