Tests for the Uniform Distribution

This chapter gives tests for a uniform distribution with unknown limits, and summarizes tests for censored uniforms. It discusses the power of the various test statistics. However, before this, some general observations can be made on the appearance of the U-set and its effect on different test statistics. The uniform distribution plays a special role in goodness-of-fit testing. When a test is made for uniformity, the alternative is often that the sample comes from a distribution which gives spacings more irregular than those from a uniform sample. The statistics so far considered have been based on various methods of relating the order statistics or their spacings to the pattern expected of them. Omnibus tests are not designed for specific alternatives, but it is convenient to mention several of these, especially for the circle, before leaving this section. Neyman found an appropriate statistic, based on likelihood ratio methods, for testing this null hypothesis.