A FORMULA FOR NORMALIZING TRANSFORMATION OF SOME STATISTICS

ABSTRACT

On the basis of Konishi's study of a normalizing transformation (Konishi [1]), a concrete normalizing transformation is derived. Some applications of the proposed normalizing transformation are shown, and performance of the transformation in the applications is numerically investigated.

Keywords:

• Chi-squared distribution
• Multinomial goodness-of-fit test
• Normalizing transformation
• Poisson distribution
• Power approximation
• Sample covariance matrix

ACKNOWLEDGMENTS

The authors are greatly indebted to reviewers for their valuable comments. This research was partly supported by Grant-in-Aid for Scientific Research, No. 11308010, Japan Society for the Promotion of Science.