Preprint
A generalization of Student’s t-distribution from the viewpoint of special functions
Zusammenfassung
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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@article{urn:nbn:de:hebis:34-2006060612898,
author={Koepf, Wolfram and Masjed-Jamei, Mohammad},
title={A generalization of Student’s t-distribution from the viewpoint of special functions},
year={2005}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2005$n2005 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-2006060612898 3000 Koepf, Wolfram 3010 Masjed-Jamei, Mohammad 4000 A generalization of Student’s t-distribution from the viewpoint of special functions / Koepf, Wolfram 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-2006060612898=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; 05, 17 5550 {{t-Verteilung}} 5550 {{Normalverteilung}} 5550 {{Gammaverteilung}} 7136 ##0##urn:nbn:de:hebis:34-2006060612898
2006-06-06T09:11:01Z 2006-06-06T09:11:01Z 2005 urn:nbn:de:hebis:34-2006060612898 http://hdl.handle.net/123456789/2006060612898 2086005 bytes application/pdf eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Normalverteilung Gammaverteilung Chi-Quadrat-Verteilung t-Verteilung Probability distributions Cauchy integral Dominated convergence theorem Pearson distribution family Fisher F-distribution 510 A generalization of Student’s t-distribution from the viewpoint of special functions Preprint 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. open access Koepf, Wolfram Masjed-Jamei, Mohammad Mathematische Schriften Kassel ;; 05, 17 60E05 62E20 33C45 t-Verteilung Normalverteilung Gammaverteilung Mathematische Schriften Kassel 05, 17
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