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Title: A generalization of Student’s t-distribution from the viewpoint of special functions
Authors: Koepf, WolframMasjed-Jamei, Mohammad
???metadata.dc.subject.swd???: t-VerteilungNormalverteilungGammaverteilung
???metadata.dc.subject.ddc???: 510 - Mathematik (Mathematics)
Issue Date: 2005
Series/Report no.: Mathematische Schriften Kassel05, 17
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.
URI: urn:nbn:de:hebis:34-2006060612898
Appears in Collections:Mathematische Schriften Kassel

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