Exact likelihood inference for two exponential populations based on a joint generalized Type-I hybrid censored sample

Abstract

Following the work of Chen and Bhattacharyya [Exact confidence bounds for an exponential parameter under hybrid censoring. Comm Statist Theory Methods. 1988;17:1857–1870], several results have been developed regarding the exact likelihood inference of exponential parameters based on different forms of censored samples. In this paper, the conditional maximum likelihood estimators (MLEs) of two exponential mean parameters are derived under joint generalized Type-I hybrid censoring on the two samples. The moment generating functions (MGFs) and the exact densities of the conditional MLEs are obtained, using which exact confidence intervals are then developed for the model parameters. We also derive the means, variances, and mean squared errors of these estimates. An efficient computational method is developed based on the joint MGF. Finally, an example is presented to illustrate the methods of inference developed here.

Keywords:

• conditional MLEs
• exact confidence interval
• exponential distribution
• joint generalized Type-I hybrid censoring
• likelihood inference
• MSEs

Acknowledgements

We express our sincere thanks to the Associate Editor, Professor Richard G. Krutchkoff, and the anonymous reviewers for their useful comments and suggestion on an earlier version of this manuscript which led to this improved version.

Disclosure statement

No potential conflict of interest was reported by the authors.