A Likelihood-Based Approximation to the Cumulative Distribution Function of the Noncentral t Distribution

Abstract

Wong (2008) proposed a third-order likelihood-based method to approximate the p-value function of any scalar parameter of the exponential family model. In this article, the method is applied to derive a simple and accurate approximation to the cumulative distribution function of the noncentral t distribution. This approximation exhibits remarkable accuracy even when the degrees of freedom is small and it does not depend on the magnitude of the non centrality.

Keywords:

• Canonical parameter
• Exponential family model
• Lugannani and Rice formula
• p-value function
• Signed log-likelihood ratio statistic

Mathematics Subject Classification:

• 62E17

Acknowledgments

The Natural Sciences and Engineering Research Council of Canada has provided support for this research. We express sincere thanks to the Editor, Associate Editor, and referees for many helpful comments and corrections.