Isotonic inference for populations related to the uniform distribution

Abstract

Consider the class of densities defined by Hogg and Craig (1956) and related to the uniform distribution, depending on an unknown parameter. Let there be k > 2 given populations yielding samples of unequal sizes from such densities. Now let a partial order on the set of the value defining the populations be given. we treat isotonic estimation, testing for order restrictins, and testing for homogeneity against order restrictions. The exact distrubutions of these tests turn out to be similar in structure to those for the normal distrubution case as iven in Barlow, Bartholomew, Bremner and Brunk (1972) and in Robertson and wegman (1978), in that they can be expressed as weighted chi square distributions. applications to selection and ranking methodlogy are pointed out.

Keywords:

• likelihood ratio
• order reatrictions
• uniform distribution
• seletin and ranking