Sequential Estimation

Summary The literature on sequential estimation is reviewed, with special reference to inverse binomial sampling, double sampling, and asymptotic theory. An approximate distribution for the sample size is found for a certain type of sequential sampling rule, in which a cumulative sum of independent random variables all having the same continuous distribution is plotted against their number until a fixed boundary is first reached or crossed. Approximate methods are given for solving a number of particular problems, including (i) estimating the mean of a normal population by a confidence interval of prescribed width and coefficient, when the population variance is unknown, and (ii) estimating the parameters of a simple birth-death process so that the difference between the birth rate and the death rate is estimated with prescribed standard error. The possible usefulness of sequential estimation procedures is discussed.