ABSTRACT
So far, we have discussed a large number of multistage methodologies of fixed-width confidence intervals for a parameter in a variety of continuous probability distributions. But, so far, we have hardly said anything about constructing fixed-width intervals for a parameter in a discrete probability distribution. That is going to change now. We will focus on probability distributions involving only a single un-
known parameter θ. We will assume that we can find a maximum likelihood estimator (MLE), θ̂n ≡ θ̂n(X1, . . . ,Xn), based on i.i.d. observations X1, . . . ,Xn from a one-parameter family of distributions. Under mild regularity conditions, Khan’s (1969) general sequential approach will apply. In Section 9.2, we provide an elementary introduction to Khan’s (1969) general sequential strategy. That would allow us to construct fixed-width confidence intervals for θ. In Section 9.3, we include an accelerated version of the sequential fixed-
width interval strategy for θ. Operationally, an accelerated sequential procedure for θ will be more convenient to apply. Section 9.4 will provide examples including binomial and Poisson distributions. We also discuss a not-so-standard example from a continuous distribution. All sequential and accelerated sequential fixed-width interval strategies
will satisfy desirable first-order asymptotic properties. Section 9.5 is devoted to data analyses and concluding remarks. Selected derivations are presented in Section 9.6.
