An approximation for Student's t-distribution

Abstract

The tail area of the t-distribution is approximated by the reciprocal of a polynomial, the coefficients being smooth functions of the reciprocal of the degrees of freedom. Sometimes it is convenient to have a numerical approximation to the tail probability of Student’s t-distribution at various degrees of freedom. An obvious approach is to assume the form used by Hastings(1955) to approximate the tail probability of the normal distribution, viz. a polynomial raised to a large negative power, and to choose the coefficients to minimize the maximum error. If this is done, it is found