A generalization of Student’s t-distribution from the viewpoint of special functions
| dc.date.accessioned | 2006-06-06T09:11:01Z | |
| dc.date.available | 2006-06-06T09:11:01Z | |
| dc.date.issued | 2005 | |
| dc.identifier.uri | urn:nbn:de:hebis:34-2006060612898 | |
| dc.identifier.uri | http://hdl.handle.net/123456789/2006060612898 | |
| dc.format.extent | 2086005 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.language.iso | eng | |
| dc.rights | Urheberrechtlich geschützt | |
| dc.rights.uri | https://rightsstatements.org/page/InC/1.0/ | |
| dc.subject | Normalverteilung | ger |
| dc.subject | Gammaverteilung | ger |
| dc.subject | Chi-Quadrat-Verteilung | ger |
| dc.subject | t-Verteilung | ger |
| dc.subject | Probability distributions | eng |
| dc.subject | Cauchy integral | eng |
| dc.subject | Dominated convergence theorem | eng |
| dc.subject | Pearson distribution family | eng |
| dc.subject | Fisher F-distribution | eng |
| dc.subject.ddc | 510 | |
| dc.title | A generalization of Student’s t-distribution from the viewpoint of special functions | eng |
| dc.type | Preprint | |
| dcterms.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. | eng |
| dcterms.accessRights | open access | |
| dcterms.creator | Koepf, Wolfram | |
| dcterms.creator | Masjed-Jamei, Mohammad | |
| dcterms.isPartOf | Mathematische Schriften Kassel ;; 05, 17 | ger |
| dc.subject.msc | 60E05 | eng |
| dc.subject.msc | 62E20 | eng |
| dc.subject.msc | 33C45 | eng |
| dc.subject.swd | t-Verteilung | ger |
| dc.subject.swd | Normalverteilung | ger |
| dc.subject.swd | Gammaverteilung | ger |
| dcterms.source.journal | Mathematische Schriften Kassel | ger |
| dcterms.source.volume | 05, 17 |
