Bayesian Inference on General-Order Statistic Models
Suppose there is a closed population of size N. In this chapter, we consider the estimation of N based on Type-I censored data. The problem is the following. Let T 1 , … , T N be a random sample of a positive random variable having the positive probability density function (PDF) at x = f ( x ; δ ) . In this case, N and δ both are unknown; moreover, δ may be vector valued also. Let T* be a prefixed time, denoting the period of observations. Suppose we 164observe 0 < t ( 1 ) < ⋯ < t ( r ) < T * within the observation period T*. There is no failure between t (r) and T*. We would like to draw the inference on N and δ, based on the above Type-I censored sample.