Approximation to Student's t Distribution in Terms of Hermite and Laguerre Polynomials

An approximation to the sampling distribution of student's 't' in the case of a non-normal population was given by Gayen [4]. He started with the first four terms of a Gram-charlier series expansion of the probability density function of the population, thereby ignoring population cumulants of order greater than four and the square and higher powers of the fourth cumulant.