The failure of electric feeders is a common problem in the summer season in Pakistan. In this article, one of the troubling aspects of the electric power system of Pakistan (Multan city) has been studied. The time lapses between the breakdown of electric feeders of the city have been modeled by suggesting an inverse Rayleigh-exponential distribution. The parameters of the distribution are estimated in both the frequentist and Bayesian paradigms. Since the Bayes estimators under informative priors are not attained in the closed form, this paper provides a comparative analysis of the Bayes estimators under Lindley and Tierney–Kadane approximation methods. The simulation study and the real-life data set assessed the validity of the model and the superiority of the Bayes estimators over the maximum likelihood estimators.
This paper explores the Lomax-Gumbel {Frechet} distribution in the Bayesian paradigm. The posterior distributions of the parameters are not attained in closed form, so the Lindley and the Tierney-Kadane approximation methods are used for the evaluation of Bayes estimators and associated posterior risks under uniform, Maxwell, and half logistic priors. A complete implementation of these two techniques is provided. Three loss functions are used. An extensive simulation study and two real life data are provided to obtain and compare Bayes estimators in terms of prior distributions and loss functions. It is reported that the Bayes estimators obtained through the Tierney-Kadane method give better results than the Lindley approximation method, in terms of minimum posterior risks.
We derived, a new three parameters continuous probability distribution called Exponentiated Transmuted Inverse Rayleigh Distribution (ETIRD). Various mathematical properties of the new distribution including mean, rth moments, moment generating function, quantile function etc. are derived. In the Classical paradigm, the estimators of the distribution are obtained using the maximum likelihood method. The Bayes estimators are derived under square error loss function (SELF) using non-informative and informative priors via the Lindley approximation technique. Bayes Estimators are compared with their corresponding maximum likelihood Estimators (MLEs) using a Monte Carlo Simulation Study under different sample sizes, different values of true parameters, using informative and non-informative priors. Performance of Bayes estimators and classical estimates is judged for the four real life data sets. The results of simulation study and real-life example show that the Bayes estimators provided better results than MLEs.
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