Journal article
A generalization of Student's t-distribution from the viewpoint of special functions
Publication Details
Authors: | Koepf, W.; Masjed-Jamei, M. |
Publication year: | 2006 |
Journal: | Integral Transforms and Special Functions |
Pages range : | 863-875 |
Volume number: | 17 |
Start page: | 863 |
End page: | 875 |
ISSN: | 1065-2469 |
Abstract
Student's t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution 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 t-distribution 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 F-distribution has a close relationship with the t-distribution, we also introduce a generalization of the F-distribution and prove that it converges to the chi-square distribution as the number of samples tends to infinity. Finally, some particular sub-cases of these distributions are considered.
Student's t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution 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 t-distribution 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 F-distribution has a close relationship with the t-distribution, we also introduce a generalization of the F-distribution and prove that it converges to the chi-square distribution as the number of samples tends to infinity. Finally, some particular sub-cases of these distributions are considered.
