| Skew t distribution and its moments |
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| 作者姓名： | Saralees NADARAJAH Arjun K. GUPTA |
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| 作者单位： | 1. Department of Statistics, University of Nebraska, Lincoln, NE 68583, USA; 2. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA |
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| 摘 要： | A random variable X is said to have the skew-t distribution if its pdf is f(x)=2g(x)G(λx), where g(?) and G(?), respectively, denote the pdf and the cdf of the Student’s t distribution with degrees of freedom ν. The moments of this distribution appear not to have been studied in detail. In this paper, we derive general expressions for the nth moment of X by considering the cases ν odd and ν even separately. These expressions turn out to involve sums of the Gauss hypergeometric function. We also provide closed form expressions for the moments of X for the particular cases ν=2,…,10.
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| 关 键 词： | complete elliptical integral of the first kind complete elliptical integral of the second kind Gauss hypergeometric function moments skew t distribution. |
Skew t distribution and its moments |
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| Saralees NADARAJAH,Arjun K. GUPTA.Skew t distribution and its moments[J].Progress in Natural Science,2006,16(10):1033-1037. |
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| Authors: | Saralees NADARAJAH Arjun KGUPTA |
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| Institution: | 1. Department of Statistics,University of Nebraska,Lincoln,NE 68583,USA
2. Department of Mathematics and Statistics,Bowling Green State University,Bowling Green,OH 43403,USA |
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| Abstract: | A random variable X is said to have the skew- t distribution if its pdf is f (x) = 2g (x) G (λx), where g (·) and G(·), respectively, denote the pdf and the cdf of the Student's t distribution with degrees of freedom ν. The moments of this distribution appear not to have been studied in detail. In this paper, we derive general expressions for the nth moment of X by considering the cases ν odd and ν even separately. These expressions turn out to involve sums of the Gauss hypergeometric function. We also provide closed form expressions for the moments of X for the particular cases ν = 2, …, 10. |
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| Keywords: | complete elliptical integral of the first kind complete elliptical integral of the second kind Gauss hypergeometric function moments skew t distribution |
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