Bayesian sequential estimation of the ratio of failure rates of two exponential distributions censored data

Abstract

This paper provides a sequential procedure for estimating the ratio of failure rates of two independent exponential distributions, using censored data. A Bayesian approach is used with gamma priors to construct a stopping time which minimizes the expected total loss plus cost of observing the process. The optimality of the proposed stopping time is established with the aid of Dynkin's identity for Markov processes.

Keywords:

• Bayes estimator
• censored data
• Dynkin's identity
• exponential distribution
• gamma prior
• Markov process
• posterior expected loss
• stopping time