On a confidence interval of given length for the parameter of the binomial and the Poisson distributions

Summary The length of the confidence interval which is constructed by one stage sampling is a random variable, whereas we can construct a confidence interval of given length and of given confidence coefficient by a sequential sampling. Of cource, the sample size required by this method is a random variable. This type of problem has already been discussed in several papers when the population is normal (see references [2], [3], [4]). In this paper we shall discuss this subject in the binomial and Poisson cases.