Bayes Estimation of the Reliability Function of Pareto Distribution Under Three Different Loss Functions

  • Gaurav Shukla Department of Statistics, Banda University of Agriculture & Technology, Banda, India
  • Umesh Chandra Department of Computer Science, Banda University of Agriculture & Technology, Banda, India
  • Vinod Kumar Department of Mathematics, Statistics & Computer Science, G.B. Pant University of Agriculture & Technology, Pantnagar, India
Keywords: Bayes estimator, maximum likelihood estimator, reliability function, prior, shape parameter, squared error loss function, quadratic loss function, asymmetric precautionary loss function

Abstract

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.

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Author Biographies

Gaurav Shukla, Department of Statistics, Banda University of Agriculture & Technology, Banda, India

Gaurav Shukla has received his M.Sc and Ph.D. (Statistics) Degree from M.J.P. Rohilkhand University, Bareilly (U.P.). He is working as an Assistant Professor in the Department of Statistics, Banda University of Agriculture and Technology, Banda, U.P. He has published 20 papers in the reputed International and National Journals. He has over 10 years of experience of teaching and research in the field of Statistics.

Umesh Chandra, Department of Computer Science, Banda University of Agriculture & Technology, Banda, India

Umesh Chandra has received his Ph.D. Degree from IIT Roorkee. He has over 6 years of experience of teaching and research in the diverse field of computer science. Currently, he is working as an assistant professor in the Department of Computer Science, Banda University of Agriculture and Technology, Banda, U.P. He has published number of papers in the reputed International and National Journal and Conferences. He has also registered six software copyrights for developing the diverse application in the field of computer application.

Vinod Kumar, Department of Mathematics, Statistics & Computer Science, G.B. Pant University of Agriculture & Technology, Pantnagar, India

Vinod Kumar completed M.Stat. and Ph.D. (Statistics) from Institute of Social Sciences, Agra University, Agra. He joined Department of Mathematics, Statistics and Computer Science, G. B. Pant University of Agriculture and Technology as Senior Statistician/Associate Professor in April, 2008 and is working as Professor of Statistics there since April, 2011. He has also served Bareilly College, Bareilly as Lecturer and Reader in the Department of Statistics from December 1986 to March 2008. He has published 37 research papers in National and International Journals.

Published
2020-11-02
Section
Articles