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

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.