Comparing the Bayesian Estimate of a Failure Rate with the Failure Rate of a Mixed Distribution

Abstract

This paper is intended to compare between the Bayesian estimate of a failure rate and the failure rate of a mixed distribution. For the sake of simplification, an exponential distribution and a gamma distribution are adopted as a sampling distribution and its natural conjugate prior distribution. The result shows that both the failure rates are being updated using data and they differ in whether they are functions of unobserved future data or not.