SEQUENTIAL CONFIDENCE INTERVALS FOR A POPULATION SIZE WITH FIXED PROPORTIONAL ACCURACY

Abstract

Consider a population of hidden objects of which the total number N is unknown. A search for the objects may be conducted in which the times at which the objects were found is recorded, along with the total number of objects found. From such data, a confidence interval for N is desired with specified proportional accuracy. Two sequential sampling plans are proposed for this problem, for two sets of underlying assumptions, and their properties are studied through asymptotic analysis and simulation.

Keywords:

• Brownian motion
• Convergence in distribution
• Exponential distributions
• Hidden objects
• Order statistics
• Poisson processes
• Simulation
• Stopping times

ACKNOWLEDGMENTS

The research of the second author was supported by the National Science Council of Taiwan and the National Science Foundation; that of the third was supported by the U.S. Army.