Maximum Likelihood Estimation under a Successive Sampling Discovery Model

Abstract

A common problem encountered in the analysis of discovery data is the size-bias phenomenon in which the larger units tend to be discovered first. One approach to account for this bias is to model the discovery process as sampling successively from a finite population without replacement and with probability proportional to size. We consider in this article a generalized version of this model for analyzing multivariate data with any given measure of size. We assume a superpopulation framework and develop procedures for maximum likelihood estimation of the parameters of the distribution. The use of the EM algorithm for computing the maximum likelihood estimates, associated computational issues, and relationships to regression estimators in survey sampling are discussed. Oil discovery data from the Rimbey—Meadowbrook reef play are used to illustrate the techniques.