Exact inference on multiple exponential populations under a joint type-II progressive censoring scheme

ABSTRACT

Recently Mondal and Kundu [Mondal S, Kundu D. A new two sample type-II progressive censoring scheme. Commun Stat Theory Methods. 2018. doi:10.1080/03610926.2018.1472781] introduced a Type-II progressive censoring scheme for two populations. In this article, we extend the above scheme for more than two populations. The aim of this paper is to study the statistical inference under the multi-sample Type-II progressive censoring scheme, when the underlying distributions are exponential. We derive the maximum likelihood estimators (MLEs) of the unknown parameters when they exist and find out their exact distributions. The stochastic monotonicity of the MLEs has been established and this property can be used to construct exact confidence intervals of the parameters via pivoting the cumulative distribution functions of the MLEs. The distributional properties of the ordered failure times are also obtained. The Bayesian analysis of the unknown model parameters has been provided. The performances of the different methods have been examined by extensive Monte Carlo simulations. We analyse two data sets for illustrative purposes.

KEYWORDS:

• Type-II censoring scheme
• progressive censoring scheme
• maximum likelihood estimator
• bootstrap confidence interval
• conjugate prior

AMS SUBJECT CLASSIFICATIONS:

• 62N01
• 62N02
• 62F10

Acknowledgments

The authors would like to thank two unknown reviewers and also the associate editor for many constructive suggestions which have helped to improve the paper significantly.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Part of the work of the second author has been supported by a grant from the Science and Engineering Research Board, Government of India, no. MTR/2018/000179.