Two-stage sampling for estimating the mean of a negative binomial distribution

Abstract

We are dealing with the problems of estimating the mean of a negative binomial distribution. We propose various types of two stage sampling techniques for controlling the coefficient of variation or the construction of confidence intervals of prescribed accuracy. Asymptotic properties are derived, and the small sample performances are studied and contrasted with those of the purely sequential procedures of Willson and Folks (1983). In many situations, our new two stage procedures perform better.

Keywords:

• Asymptotios
• coefficient of variation
• fixed-width interval
• proportional closeness
• simulations