Goodness-of-fit analysis for uniformity in a bounded solid region

摘要

The test statistic X² for uniformity in a bounded solid region D1 is suggested. The sufficient and necessary condition for the uniform distribution in D1 is proved, the asymptotic chi squared distribution of X² is obtained, the consistency of the goodness-of-fit tests is proved. The simulation of the convergence rate of the empirical distribution function and the test power is made, the simulation results show that the multivariate goodness-of-fit tests for sample size n ≥ 10 is effective.