Communications in statistics-simulation and computation vol:26 issue:3 pages:1029-1039
In this paper, we obtain a new approximation of the Student's t distribution by using the symmetric generalized logistic (SGL) distribution function. The error of this approximation is shown to be O(1/n(2)) where n is the degrees of freedom of the t distribution. In comparison to similar approximations by George and Ojo(1980) and George et al. (1986), this new approximation is much simpler and more accurate. It is also shown that under some conditions, the t distribution is a good approximation of the SGL distribution. Therefore, the complicated expressions for the cumulants and moments of the SGL can be approximated by those of the t distribution. Finally, numerical results are given.