On partially observed competing risk model under generalized progressive hybrid censoring for Lomax distribution

ABSTRACT

We study a competing risks model under the assumption that latent failure times follow family of Lomax distributions. We obtain various inferences for model parameters when causes of failure are partially known and lifetime data are observed using a generalized progressive hybrid censoring scheme. The existence and uniqueness properties of maximum likelihood estimators of unknown parameters are established. Bayes estimators and associated credible intervals are also obtained. In addition, various inferences for unknown parameters are derived under order-restricted shape parameters of Lomax distributions. Finally, a simulation study is conducted to evaluate the performance of the proposed estimates. A real data set is also analysed for illustration purposes.

KEYWORDS:

• Competing risks
• Bayes estimate
• Fisher information matrix
• HPD interval
• maximum likelihood estimate
• order restriction

Acknowledgments

The authors would like to thank referees and the editor for their insightful comments that have led to a substantial improvement to an earlier version of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work of Liang Wang was supported by the National Natural Science Foundation of China (No. 12061091), the Yunnan Fundamental Research Projects (No. 202101AT070103) and the Doctoral Research Foundation of Yunnan Normal University (No. 00800205020503129).

Notes on contributors

Amulya Kumar Mahto

Dr. Amulya Kumar Mahto is an assistant professor at Kalinga Institute of Industrial Technology, Bhubaneswar, India. He received his PhD in Statistics and MTech in Mathematics and Computing from Indian Institute of Technology, Patna, India and MSc in Mathematics and Computing from Indian School of Mines, Dhanbad, India. His research interest includes accelerated life testing, competing risks, multicomponent stress-strength reliability and has published number of research papers in journals of repute. His research interest also extends to transfer learning.Dr. Amulya Kumar Mahto is an assistant professor at Kalinga Institute of Industrial Technology, Bhubaneswar, India. He received his PhD in Statistics and MTech in Mathematics and Computing from Indian Institute of Technology, Patna, India and MSc in Mathematics and Computing from Indian School of Mines, Dhanbad, India. His research interest includes accelerated life testing, competing risks, multicomponent stress-strength reliability and has published number of research papers in journals of repute. His research interest also extends to transfer learning.

Chandrakant Lodhi

Chandrakant Lodhi is a Data Scientist at neuriot technologies LLP, Gurugram, Haryana, India. He received his Ph.D. degree in statistics from the Department of Mathematics, IIT Patna, Bihar, India. He also did MTech in Mathematics and Computing from IIT Patna, Bihar, India. His research interests are statistical inference, reliability inference, competing risk analysis, and optimal design of censored life testing experiments.

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. Éric 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.

Liang Wang

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