A modification of the fisher-cornish approximation for the student t percentiles
An asymptotic expansion of the Student t distribution is derived by expanding the standardized Student t distribution in terms of the normal distribution. This expansion is inverted to obtain corresponding asymptotic expansions for the Student t percentiles as functions of the standard normal percentiles Using the first two, three or four terms of these expansions, we get approximations of the Student t percentiles which are generally more accurate than the approximations given by Fisher and Cornish (1960) and Koehler (1983). An approximation of the distribution function obtained from this expansion is compared with the approximations discussed by Ling (1978) and found to be more accurate for moderate degrees of freedom. Copyright © 1987 by Marcel Dekker, Inc.
Communications in Statistics - Simulation and Computation
George, E., & Sivaram, M. (1987). A modification of the fisher-cornish approximation for the student t percentiles. Communications in Statistics - Simulation and Computation, 16 (4), 1123-1132. https://doi.org/10.1080/03610918708812641