New asymptotic representations of the noncentral t-distribution

Abstract

New asymptotic approximations of the noncentral t distribution are given a generalization of the Student's t distribution. Using new integral representations, we give new asymptotic expansions not only for large values of the noncentrality parameter but also for large values of the degrees of freedom parameter. In some cases, we accept more than one large parameter. These results are not only in terms of elementary functions, but also in terms of the complementary error function and the incomplete gamma function. A number of numerical tests demonstrate the performance of the asymptotic approximations.