Tail Approximation of the Skew-Normal by the Skew-Normal Laplace: Application to Owen’s T Functionand the Bivariate Normal Distribution

By equal mean, two skew-symmetric families with the same kernel are quite similar, and the tails are often very close together. We use this observation to approximate the tail distribution of the skew-normal by the skew-normal-Laplace, and accordingly obtain a normal function approximation to Owen’s T function, which determines the survival function of the skew-normal distribution. Our method is also used to derive skew-normal-Laplace approximations to the bivariate standard normal distribution valid for large absolute values of the arguments and correlation coefficients, a situation difficult to handle with traditional numerical methods.