Aufsatz in einer Fachzeitschrift
A generalization of Student's t-distribution from the viewpoint of special functions



Details zur Publikation
Autor(inn)en:
Koepf, W.; Masjed-Jamei, M.
Publikationsjahr:
2006
Zeitschrift:
Integral Transforms and Special Functions
Seitenbereich:
863-875
Jahrgang/Band:
17
Erste Seite:
863
Letzte Seite:
875
ISSN:
1065-2469

Zusammenfassung, 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.


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Zuletzt aktualisiert 2019-01-11 um 16:05