Selection of suitable prior for the Bayesian mixture of a class of lifetime distributions under type-I censored datasets

Abstract

This paper explores the study on mixture of a class of probability density functions under type-I censoring scheme. In this paper, we mold a heterogeneous population by means of a two-component mixture of the class of probability density functions. The parameters of the class of mixture density functions are estimated and compared using the Bayes estimates under the squared-error and precautionary loss functions. A censored mixture dataset is simulated by probabilistic mixing for the computational purpose considering particular case of the Maxwell distribution. Closed-form expressions for the Bayes estimators along with their posterior risks are derived for censored as well as complete samples. Some stimulating comparisons and properties of the estimates are presented here. A factual dataset has also been for illustration.

Keywords:

• finite mixture of a class of lifetime distributions
• censored sampling
• fixed termination time
• limiting expressions
• elicitation of hyperparameter
• squared-error loss function
• precautionary loss function

Acknowledgements

The authors wish to thank the Chief Editor Dr Robert G Aykroyd and other respectable reviewers for providing us useful comments in order to present this research in a beautiful manner. Executive Director Dr AbidSuleri (Sustainable Development Policy Institute, Islamabad, Pakistan) also deserves special thanks for his moral support and encouragement throughout the research work.