Odd log-logistic generalised Lindley distribution with properties and applications

Vahid Ranjbar; Abbas Eftekharian; Omid Kharazmi; Morad Alizadeh

doi:https://doi.org/10.59170/stattrans-2023-052

Odd log-logistic generalised Lindley distribution with properties and applications

Vahid Ranjbar Golestan University, Gorgan, Iran ORCID:https://orcid.org/0000-0003- 3743-0330 , Abbas Eftekharian University of Hormozgan, Bandar Abbas, Iran ORCID:https://orcid.org/0000-0002-5343-8597 , Omid Kharazmi Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran ORCID:https://orcid.org/0000-0003-4176-9708 , Morad Alizadeh Persian Gulf University, Bushehr, Iran ORCID:https://orcid.org/0000-0001-6638-2185 Statistics in Transition new series, vol. 24, 2023, 4, pages: 71-92 Published online: 8 September 2023 https://doi.org/10.59170/stattrans-2023-052 Citation: Ranjbar, V., Eftekharian, A., Kharazmi, O., Alizadeh, M., 2023. Odd log-logistic generalised Lindley distribution with properties and applications. Statistics in Transition new series, 24(4), pp. 71-92. https://doi.org/10.59170/stattrans-2023-052

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ABSTRACT

In this paper, a new three-parameter lifetime model, called the odd log-logistic generalised Lindley distribution, is introduced. Some structural properties of the new distribution including ordinary and incomplete moments, quantile and generating functions and order statistics are obtained. The new density function can be expressed as a linear mixture of exponentiated Lindley densities. Different methods are discussed to estimate the model parameters and a simulation study is carried out to show the performance of the new distribution. The importance and flexibility of the new model are also illustrated empirically by means of two real data sets. Finally, Bayesian analysis and Gibbs sampling are performed based on the two real data sets.

KEYWORDS

Lindley distribution, odd log-logistic generalised family, moments, Bayesian analysis, simulation study

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