A study on exponentiated Gompertz distribution under Bayesian discipline using informative priors

Muhammad Aslam; Mehreen Afzaal; M. Ishaq Bhatti

doi:10.21307/stattrans-2021-040

A study on exponentiated Gompertz distribution under Bayesian discipline using informative priors

Muhammad Aslam Department of Mathematics and Statistics, Riphah International University, Pakistan ORCID:https://orcid.org/0000-0003-3355-2330 , Mehreen Afzaal Department of Mathematics and Statistics, Riphah International University, Pakistan ORCID:https://orcid.org/0000-0002-1550-3415 , M. Ishaq Bhatti La Trobe Business School, La Trobe University, Australia ORCID:https://orcid.org/0000-0002-5027-7871 Statistics in Transition new series, vol. 22, 2021, 4, pages: 101-119 Published online: 8 December 2021 DOI 10.21307/stattrans-2021-040

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ABSTRACT

The exponentiated Gompertz (EGZ) distribution has been recently used in almost all areas of human endeavours, starting from modelling lifetime data to cancer treatment. Various applications and properties of the EGZ distribution are provided by Anis and De (2020). This paper explores the important properties of the EGZ distribution under Bayesian discipline using two informative priors: the Gamma Prior (GP) and the Inverse Levy Prior (ILP). This is done in the framework of five selected loss functions. The findings show that the two best loss functions are the Weighted Balance Loss Function (WBLF) and the Quadratic Loss Function (QLF). The usefulness of the model is illustrated by the use of reallife data in relation to simulated data. The empirical results of the comparison are presented through a graphical illustration of the posterior distributions.

KEYWORDS

exponentiated Gompertz distribution, loss functions, informative priors, Bayes estimators, posterior risks

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