Abstract
The q-Weibull distribution is a generalized form of the Weibull distribution and has potential to model complex systems and life time datasets. Bayesian inference is the modern statistical technique that can accommodate uncertainty associated with the model parameters in the form of prior distributions. This study presents Bayesian analysis of the q-Weibull distribution using uninformative and informative priors and the results are compared with those produced by the classical maximum likelihood (ML) and least-squares (LS) estimation methods. A simulation study is also made to compare the competing methods. Different model selection criteria and predicted datasets are considered to compare the inferential methods under study. Posterior analyses include evaluating posterior means, medians, credible intervals of highest density regions, and posterior predictive distributions. The entire analysis is carried out using Markov chain Monte Carlo (MCMC) setup using WinBUGS package. The Bayesian method has proved to be superior to its classical counterparts. A real dataset is used to illustrate the entire inferential procedure.
Highlights
Several q-type distributions are proposed to model complex systems appearing in the fields of biology, chemistry, economics, geography, informatics, linguistics, mathematics, medicine, physics, etc. [1⚶3]
When there is sufficient information available about the model parameters, it becomes necessary to avail it by assigning informative priors to the model parameters such that they can adequately fit to the knowledge available for the model parameters being examined
The Markov chain Monte Carlo (MCMC) method can be implemented using any of the standard softwares like R, Python, etc., but the most specific software being used for the Bayesian analysis is Windows based Bayesian inference Using Gibbs Sampling (WinBUGS)
Summary
Several q-type distributions are proposed to model complex systems appearing in the fields of biology, chemistry, economics, geography, informatics, linguistics, mathematics, medicine, physics, etc. [1⚶3]. Besides modeling the complex systems, the q-W distribution has the potential to describe lifetime datasets [4,10⚶13]. It has got much popularity and is frequently used in different fields. The parameters are assumed random quantities in the Bayesian approach and follow certain probability distribution and take both the current dataset and prior information about the parameters into account. It has been established that the q-Weibull distribution is a good choice to model complex systems and lifetime datasets appearing in a variety of fields. Β, and η are unknowns parameters that control the behavior of the datasets emerging from the q-Weibull distribution Estimating these unknown parameters is ultimate aim of the inferential statistics. We have analyzed the q-Weibull distribution in Bayesian framework to avail the aforesaid advantages the approach
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