A Note on a General Method for Obtaining Confidence Intervals from Samples from Discrete Distributions

Using a general method available in the sampling literature, this article points out the possibility of obtaining, from samples from a discrete distribution with one unknown parameter, two-sided lower and upper confidence limits that are not well defined in the sense that the upper confidence limit is smaller than the lower confidence limit.An example is given. Sufficient conditions are derived to prevent such a problem from arising.It is also shown, in particular, that no such problem arises in the cases of the binomial and hypergeometric distributions.