Journal article
A generalization of Student's tdistribution from the viewpoint of special functions
Publication Details
Authors:  Koepf, W.; MasjedJamei, M.

Journal:  Integral Transforms and Special Functions 
Abstract
Student's tdistribution has found various applications in mathematical statistics. One of the main properties of the tdistribution is to converge to the normal distribution as the number of samples tends to infinity. In this paper, by using a Cauchy integral we introduce a generalization of the tdistribution function with four free parameters and show that it converges to the normal distribution again. We provide a comprehensive treatment of mathematical properties of this new distribution. Moreover, since the Fisher Fdistribution has a close relationship with the tdistribution, we also introduce a generalization of the Fdistribution and prove that it converges to the chisquare distribution as the number of samples tends to infinity. Finally, some particular subcases of these distributions are considered.