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

摘要

Wong (200812. Wong , A. ( 2008 ). Approximating the F distribution via a general version of the modified signed log-likelihood ratio statistic . Computational Statistics & Data Analysis 53 : 3902 - 3912 . [CrossRef]View all references) 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.