Estimating undiscovered resources using exploration history

A model for oil and gas exploration posits that exploratory wells are placed at random, sequentially, in the previously unexplored portion of an area containing petroleum fields of various sizes. Following drilling, it is often of interest to estimate the size distribution of remaining undiscovered fields or to predict the result of future exploration.;This thesis is concerned with asymptotic results for a variety of approaches to this problem under such a sampling scheme. Point estimates and confidence intervals for functionals of the distribution based on partial likelihood methods, a method of moments approach and UMVUE estimation, simultaneous confidence bands for the distribution itself and predictive intervals for the results of future exploration are discussed. Simulation results are presented.