Modifications of the kolmogorov, cramer-von mises, and watson tests for testing uniformity with unknown limits

Abstract

Modifications of the Kolmogorov, Cramér-von Mises, and Watson tests for testing uniformity with unknown limits are suggested. It is shown that the asymptotic distributions of the modified test statistics coincide with those of the respective standard versions. Precise tables of the quantiles of the modified statistics are obtained by Monte Carlo simulation for samples of small and medium size.

Keywords:

• uniform distribution
• unknown limits
• finite sample distribution
• asymptotic distribution
• simulated quantiles