International Journal of Reliability and Applications
- Volume 4 Issue 3
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- Pages.97-111
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- 2003
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- 1598-0073(pISSN)
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- 2283-8914(eISSN)
Power Exponential Distributions
- Zheng, Shimin (Department of Biostatistics, University of Alabma) ;
- Bae, Sejong (Department of Biostatistics, University of North Texas Health Science Center) ;
- Bartolucci, Alfred A. (Department of Biostatistics, University of Alabama) ;
- Singh, Karan P. (Department of Biostatistics, University of North Texas Health Science Center)
- Published : 2003.09.01
Abstract
By applying Theorem 2.6.4 (Fang and Zhang, 1990, p.66) the dispersion matrix of a multivariate power exponential (MPE) distribution is derived. It is shown that the MPE and the gamma distributions are related and thus the MPE and chi-square distributions are related. By extending Fang and Xu's Theorem (1987) from the normal distribution to the Univariate Power Exponential (UPE) distribution an explicit expression is derived for calculating the probability of an UPE random variable over an interval. A representation of the characteristic function (c.f.) for an UPE distribution is given. Based on the MPE distribution the probability density functions of the generalized non-central chi-square, the generalized non-central t, and the generalized non-central F distributions are derived.
Keywords
- multivariate power exponential distribution;
- gamma distribution;
- generalized non-central chi-square;
- generalized non-central t;
- generalized non-central F;
- characteristic function