Implementation of Upper Multinomial Bound Using Clustering

The multinomial bound is a nonparametric bound for a finite population total when most elements have a value of zero and the remaining elements have positive values, such as occur in accounting and in threshold problems in the physical and biological sciences. Up to now, computational difficulties have restricted use of the multinomial bound to cases where the sample contains eight or less errors. The use of clustered errors described in this paper extends use of the multinomial bound to cases where the sample contains up to 25 errors, with only moderate loss in tightness of the bound.