Inference and optimal design for doubly censored data using generalized lifetime distribution family

Abstract

In this paper, we address the challenging problem of statistical inference for unknown parameters in generalized lifetime distributions under double censoring. We propose classical and Bayesian estimation approaches for these parameters, incorporating a range of loss functions in the Bayesian framework to improve flexibility and estimate accuracy. The Bayesian inference is implemented using the Metropolis-Hastings algorithm within a Markov Chain Monte Carlo setting to generate posterior samples. These samples are subsequently utilized to compute Bayes estimates and construct credible intervals, thereby providing a comprehensive measure of parameter uncertainty. The performance of the proposed methods is systematically evaluated through simulation studies, which assess their accuracy under various censoring schemes. Additionally, we present two real-data examples to illustrate the practical applicability and utility of the methods in addressing doubly censored data. Furthermore, we explore optimal experimental design considerations, proposing experimental plans specifically tailored to the double-censoring structure. This study offers new insights into the design and analysis of experiments where double censoring is prevalent, with the potential to optimize both time and resource allocation in such studies.

Keywords

• Bayesian inference
• Bayesian optimal design
• generalized lifetime distribution family
• maximum likelihood estimation
• MCMC algorithm

Supporting Institution

The research work of Chandan Kumar Gupta is partially supported under a grant PMRF-ID: 2702855 and Yogesh Mani Tripathi is partially supported under a grant MTR/2022/000183 by Science and Engineering Research Board, India.

Thanks

The authors thank the Editor and an Associate Editor for helpful comments that improved the manuscript. They also thank the reviewers for their useful comments, which substantially improved the content and presentation of the manuscript. This work of Chandan Kumar Gupta is financially supported by the Prime Minister’s Research Fellowship scheme, Ministry of Education, Govt. of India, under PMRF-ID: 2702855, and the research work of Yogesh Mani Tripathi is partially financially supported under a grant MTR/2022/000183 by the Science and Engineering Research Board, India.

References

1. [1] M. G. Akritas, S. A. Murphy and M. P. Lavalley, The Theil-Sen estimator with doubly censored data and applications to astronomy, J. Am. Stat. Assoc. 90 (429), 170-177, 1995.