Generalized extended Marshall-Olkin family of lifetime distributions

Mehdi Goldoust; Adel Mohammadpour

doi:10.21307/stattrans-2022-004

Generalized extended Marshall-Olkin family of lifetime distributions

Mehdi Goldoust Department of Mathematics, Behbahan Branch, Islamic Azad University, Behbahan, Iran ORCID:https://orcid.org/0000-0002-5859-3350 , Adel Mohammadpour Department of Statistics, Faculty of Mathematics & Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran ORCID:https://orcid.org/0000-0002-5079-7025 Statistics in Transition new series, vol. 23, 2022, 1, pages: 55-74 Published online: 15 March 2022 DOI 10.21307/stattrans-2022-004 Citation: Goldoust M., Mohammadpour A.,(2022). Generalized extended Marshall-Olkin family of lifetime distributions, Statistics in Transition new series, 23(1), pp. 55–74. https://doi.org/10.21307/stattrans-2022-004

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ABSTRACT

We introduce a new generalized family of nonnegative continuous distributions by adding two extra parameters to a lifetime distribution, called the baseline distribution, by twice compounding a power series distribution. The new family, called the lifetime power series-power series family, has a serial arrangement of parallel structures, which extends the Marshall and Olkin structure. Four special models are discussed. A mathematical treatment of the new distributions is provided, including ordinary and incomplete moments, quantile, moment generating and mean residual functions. The maximum likelihood estimation technique is used to estimate the model parameters and a simulation study is conducted to investigate the performance of the maximum likelihood estimates. Its applicability is also illustrated by means of two real data sets.

KEYWORDS

compound distribution, hazard rate function, lifetime distribution, maximum likelihood estimation, power series distribution

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