Exact distributions of two non-central generalized Wilks's statistics

ABSTRACT

We derive the exact expressions of the probability density function (pdf) and the cumulative distribution function (cdf) of Wilks's likelihood ratio criterion Λ and Wilks-Lawley's statistic U in the non-central linear and the non-central planar cases. Those expressions are given in rapidly converging infinite series and can be used for numerical computation. For applications, we compute the exact power of these statistics in a multivariate analysis of variance exercise, and show by simulation the precision of our analytic formulae.

Keywords:

• Legendre function
• Meijer G-function
• non-central linear
• non-central planar
• non-central wilks statistic
• zonal polynomial

Acknowledgements

The authors wish to thank the associate editor and two anonymous referees for their constructive criticisms and suggestions that have helped them to improve the quality of their paper.

Disclosure statement

No potential conflict of interest was reported by the authors.