Zentralblatt MATH Database 1931 – 2009
c 2009 European Mathematical Society, FIZ Karlsruhe & Springer-Verlag
Zbl 1109.60010
Koepf, Wolfram; Masjed-Jamei, Mohammad
A generalization of Student’s t-distribution from the viewpoint of special
functions. (English)
Integral Transforms Spec. Funct. 17, No. 12, 863-875 (2006). ISSN 1065-2469; ISSN
1476-8291
http://dx.doi.org/10.1080/10652460600856419
http://www.tandf.co.uk/journals/titles/10652469.html
The authors present a generalization of Student t-distribution based on Cauchy integral; the new distribution depends on four parameters. In the same way as the classical
distribution tends to the normal law as the number of degrees of freedom goes to infinity so does the generalized distribution converge to the normal law. Mean value and
variance of the new distribution are given. A generalization of Fisher F -distribution is
also given and it is shown that it tends to the chi-square law. The last part of the paper
is devoted to the consideration of particular cases.
Carlo Sempi (Lecce)
Keywords : Student t-distribution; Cauchy integral: Fisher F -distribution; normal distribution; gamma distribution; chi-square distribution
Classification :
∗ 60E05 General theory of probability distributions
62E20 Asymptotic distribution theory in statistics
33C45 Orthogonal polynomials and functions of hypergeometric type
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