Estimation and prediction of modified progressive hybrid censored data from inverted exponentiated Rayleigh distribution

ABSTRACT

In this paper, statistical inference of an inverted exponentiated Rayleigh model is studied when the failure times are obtained under a modified progressive hybrid censoring. The maximum likelihood estimators of the model parameters together with associated existence and uniqueness are established, and approximate confidence intervals are constructed based on asymptotic theory. Alternatively, generalized point and interval estimates for unknown parameters are also constructed based on the proposed pivotal quantities for comparison. In addition, predictive intervals of remaining useful life from the inverted exponentiated Rayleigh distribution are also constructed under classical and generalized inferential approaches, respectively. Finally, extensive simulation studies are carried out to compare the performance of the proposed methods, and two real-life examples are analyzed for illustration. The numerical results indicate that both traditional likelihood and generalized inferential methods work satisfactorily, and that our proposed generalized approach appears much more appealing and are superior to classical results.

KEYWORDS:

• Inverted exponentiated Rayleigh distribution
• Modified progressive hybrid censoring
• Maximum likelihood estimates
• Generalized estimation
• remaining useful life
• prediction

Acknowledgements

The authors would like to thank the Editor and three referees for their insightful comments that have led to a substantial improvement to an earlier version of the paper. This work of Liang Wang was supported by the National Natural Science Foundation of China under Grant No. 12061091, the Yunnan Fundamental Research Projects under Grant No. 202101AT070103, and Yunnan Key Laboratory of Modern Analytical Mathematics and Applications.

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China [12061091]; Yunnan Fundamental Research Projects [202101AT070103]

Notes on contributors

Liang Wang

Liang Wang received the Ph.D. degree in Applied Mathematics from Northwestern Polytechnical University, Xi'an, China, in 2012. He is currently a full Professor with the School of Mathematics, Yunnan Normal University, Kungming, China. His research interests include applied probability and statistics, reliability analysis and life testing.

Shuo-Jye Wu

Shuo-Jye Wu is a professor in the Department of Statistics at Tamkang University. He received his PhD in statistics from the University of Wisconsin-Madison. His professional interests are in the development and application of statistical methodology for problems in reliability.

Yogesh Mani Tripathi

Yogesh Mani Tripathi received his Ph.D. degree from the Department of Mathematics, Indian Institute of Technology Kharagpur, India, under the guidance of Prof. Somesh Kumar. He was a Postdoctoral Fellow with Prof. Eric Marchand with the Department of Mathematics at University of Sherbrooke, Canada and with G. S. Shieh at Institute of Statistical Science, Academia Sinica, Taiwan. Currently, he is an Associate Professor with the Department of Mathematics, Indian Institute of Technology Patna, India. His research interests are in decision theory, life-testing and reliability analysis.

Sanku Dey

Sanku Dey PhD is currently working as Associate Professor in the Department of Statistics, St. Anthony's College, Shillong, Meghalaya, India. He did his M.Sc. in Statistics in the year of 1991 from Gauhati University, Guwahati, India and Ph.D. in Statistics (reliability theory) in the year 1998 from the same university. He has published 270 research papers in journals of repute. He is also an Academic Editor, Associate Editor and Section Editor of renowned international journals. He has a good number of contributions in almost all fields of Statistics viz, distribution theory, reliability theory, Bayesian inference, Record Statistics, Statistical quality control, order statistics, lifetime performance index based on classical and Bayesian approach as well as different types of censoring schemes etc.