Open AccessBayes Estimation of the Reliability Function of Pareto Distribution Under Three Different Loss Functions
Author(s) -
Gaurav Shukla,
Umesh Chandra,
Vijay Kumar
Publication year - 2020
Publication title -
journal of reliability and statistical studies
Language(s) - English
Resource type - Journals
eISSN - 2229-5666
pISSN - 0974-8024
DOI - 10.13052/0974-8024.1318
Subject(s) - prior probability , estimator , minimum variance unbiased estimator , bayes estimator , mathematics , bayes' theorem , statistics , gamma distribution , pareto distribution , bias of an estimator , bayesian probability , lomax distribution , reliability (semiconductor) , efficient estimator , variance (accounting) , function (biology) , pareto principle , power (physics) , physics , accounting , quantum mechanics , evolutionary biology , business , biology
In this paper, we have proposed Bayes estimators of shape parameter of Pareto distribution as well as reliability function under SELF, QLF and APLF loss functions. For better understanding of Bayesian approach, we consider Jeffrey’s prior as non-informative prior, exponential and gamma priors as informative priors. The proposed estimators have been compared with Maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE). Moreover, the current study also derives the expressions for risk function under these three loss functions. The results obtained have been illustrated with the real as well as simulated data set.