Goodness-of-fit tests for location–scale families based on random distance

Abstract

For location–scale families, we consider a random distance between the sample order statistics and the quasi sample order statistics derived from the null distribution as a measure of discrepancy. The conditional qth quantile and expectation of the random discrepancy on the given sample are chosen as test statistics. Simulation results of powers against various alternatives are illustrated under the normal and exponential hypotheses for moderate sample size. The proposed tests, especially the qth quantile tests with a small or large q, are shown to be more powerful than other prominent goodness-of-fit tests in most cases.

Keywords:

• goodness-of-fit
• regression test
• order statistics
• location–scale family

2000 AMS Subject Classification::

• Primary: 62G10
• Secondary: 62G30, 62G09