A NOTE ON OBTAINING CONFIDENCE-INTERVALS FOR DISCRETE PARAMETERS

Peskun considers the problem of constructing a closed confidence interval for a single parameter, using a discrete test statistic. The interval is constructed by generalizing the method of Konijn. Peskun gives an example where the interval fails to be well defined. In this article a confidence interval is constructed by generalizing the method of Cochran, in a manner similar to the way in which Peskun generalizes Konijn's technique. Buonaccorsi compares the Konijn and Cochran type intervals in the hypergeometric setting. This article shows that the Cochran interval is always well defined and contains the Peskun interval, and that the Cochran interval contains, at most, two points more than the Peskun interval. Discrepancies between the two kinds of intervals, and ill definition of the Peskun interval, follow from discreteness of the parameter space, rather than discreteness of the test statistic.