Bayesian Estimation of the Shape Parameter of Lomax Distribution under Uniform and Jeffery Prior with Engineering Applications

Abstract

In engineering, it is usual to model the data so as to make a decision under the problem of uncertainty. Commonly, the data in engineering is skewed to the right, and the skewed distributions in statistics are the appropriate models for making a decision under the Bayesian paradigm. To model the lifetime of an electronic device, an engineer can use the Bayesian estimators to compute the effect of the evidence in increasing the probability for the lifetime of an electronic device by using the prior information. This study presents an estimation of the shape parameter of Lomax distribution under Uniform and Jeffery prior by adopting SELF, QELF, WSELF, and the PELF. The significance of various estimators is compared and presented in graphs using simulated data under the Bayesian paradigm. It was determined that under a uniform prior, Bayes estimator under weighted error loss function (BWEL) provides a better result than others. Under Jeffery prior, the precautionary error loss function (BPEL) leads to a better result than others. Moreover, an application to engineering is also presented for illustration purposes.

Different Approaches for Outlier Detection in Life Testing Scenarios

“…Data set 2 Here, Arset data has been considered which was reported by [18], [18] and some references therein. This data represents the failure times of 50 electronic devices in weeks.The data are: The maximum likelihood estimates are obtained for the Lomax distribution as α = 2.39 and λ = 19.790.…”

“…including complete samples and various types of censored samples such as Type I and II censoring, hyper-censoring Type I and II, Generalized hyper-censoring Type I and II, and progressive Type I and Type II censoring. Examples of studies in this domain include those conducted by [4], [34], [3], [18], [20], and [19].…”