A corrected normal approximation for the student's t distribution

For the Student’s t cumulative distribution function F(x;n) with n≥3 degrees of freedom, a corrected normal approximation, Φ(λx), is proposed as an extension of the well-known ordinary normal approximation Φ(x), where Φ(x) is the standard normal cumulative distribution and λ=λ(x,n) is a shrinking factor (0<λ<1). This approximation has a theoretical error O(1/n2) uniformly in x. Numerical results show that it can give satisfactory accuracy for even very small n. Thus, it provides a competitive alternative because of its reasonable balance between accuracy and simplicity.