A Test for Normality Based on Kullback—Leibler Information

Abstract

A goodness-of-fit test (based on sample entropy) for normality was given by Vasicek. The test, however, can be applied only to the composite hypotheses. In this article an extended test of fit for normality is introduced based on Kullback—Leibler information. The Kullback—Leibler information is an extended concept of entropy, so the test can be applied not only to the composite hypotheses, but also to the simple hypotheses. The power comparisons of the proposed test with some other tests are illustrated and discussed.

Key Words:

• Entropy estimation
• Goodness-of-fit tests
• Normality tests