A Method of Sequential Estimation Applicable to the Hypergeometric, Binomial, Poisson, and Exponential Distributions

Abstract

Sequential estimation for the particular stopping rule, inverse or Haldane sampling, has been developed for the hypergeometric [4], [13], [15], binomial [10], [12], Poisson [17], and exponential [6], [16], distributions; more general stopping rules have been discussed for the binomial distribution by Girshick, Mosteller, and Savage [11] and for the exponential distribution by the author [14]. It is the purpose of this article to present a unified treatment of these distributions and to extend the known results for inverse sampling to a more general class of stopping rules called monotone. Estimates of parameters are obtained following [11], estimates of the variances of these estimates obtained, their distribution related to that of the fixed sample size stopping rule, and confidence methods suggested. Most of the methods described do not require complete knowledge of the stopping rule for their application.