Nonparametric Tolerance Regions

Abstract

Nonparametric tolerance regions can be constructed from statistically equivalent blocks using published graphs by Murphy [8]. In this paper the procedure for obtaining the statistically equivalent blocks is generalized. The $n$ `cuts' used to form the $n + 1$ blocks need not cut off one block at a time, but at each stage may cut off a group of blocks, the group to be further divided at a later stage by a different type of cut in general. An example is given which indicates possible applications. The results are also interpreted for discontinuous distributions by indicating the necessary modifications to the corresponding theorem in [7].