Goodness-of-fit testing by transforming to normality: comparison between classical and characteristic function-based methods

Abstract

Chen and Balakrishnan [Chen, G. and Balakrishnan, N., 1995, A general purpose approximate goodness-of-fit test. Journal of Quality Technology, 27, 154–161] proposed an approximate method of goodness-of-fit testing that avoids the use of extensive tables. This procedure first transforms the data to normality, and subsequently applies the classical tests for normality based on the empirical distribution function, and critical points thereof. In this paper, we investigate the potential of this method in comparison to a corresponding goodness-of-fit test which instead of the empirical distribution function, utilizes the empirical characteristic function. Both methods are in full generality as they may be applied to arbitrary laws with continuous distribution function, provided that an efficient method of estimation exists for the parameters of the hypothesized distribution.

Keywords:

• Empirical characteristic function
• Empirical distribution function
• Goodness-of-fit test

Acknowledgements

The author wishes to sincerely thank an anonymous referee for the constructive comments that led to improvement of the paper.

Notes

^†This is the only case where the large sample distribution of the CF statistic has been found theoretically.