On tests of uniformity

Abstract

Let X₁,…,X_n be independent observations from a distribution on the interval (a,b). Fur each of three types of nonuniformity, we consider tests of uniformity (a and b known) designed to detect alternatives of that type. The types of nonuniformity are (i) U-shaped, (ii) unimodal symmetric or nearly symmetric, and (iii) nonsymmetric distributions that have decreasing density or that are unimodal with mode close to a. A Monte Carlo power study is given. The application to testing the distributional hypothesis of exponentiality against specific types of nonexponentiality is discussed. An easy extension of tests of uniformity to the case of unknown endpoints is pointed out; and an investigation of power properties, including a Monte Carlo study, is given.

Keywords:

• exponentiality
• tests of
• goodness-of-fit
• monte carlo power study
• nonuniformity
• types of
• tests of distributional hypotheses