A New Goodness-of-Fit Test Based on the Empirical Characteristic Function

Abstract

In this article, we present a goodness-of-fit test for a distribution based on some comparisons between the empirical characteristic function c_n(t) and the characteristic function of a random variable under the simple null hypothesis, c₀(t). We do this by introducing a suitable distance measure. Empirical critical values for the new test statistic for testing normality are computed. In addition, the new test is compared via simulation to other omnibus tests for normality and it is shown that this new test is more powerful than others.

Keywords:

• Characteristic function
• Eigen values
• Eigen vectors
• Empirical characteristic function
• Goodness-of-fit test
• Multivariate central limit theorem
• Principal components method

Mathematics Subject Classification:

• Primary 62G10, 62H10
• Secondary 62C12, 62G20, 62H25

Acknowledgments

The authors would like to thank the referee for his constructive suggestions and also the Research Council of Shiraz University for their support.