Estimating Population Size with Exponential Failure

Abstract

We are given J observations obtained by truncated sampling of a population of N items which fail independently according to the exponential distribution, where both N and the scale parameter of the exponential are unknown. Estimates of N are developed, and compared. These are conditional and unconditional maximum likelihood estimates, and a class of Bayes modal estimates. On the basis of second-order asymptotic properties, one of the Bayes estimates is singled out as most desirable. This estimator is also good for estimating mean life, but for estimating failure rate, the maximum likelihood estimates are preferable.