The skew elliptical distributions and their quadratic forms |
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| Authors: | B Q Fang |
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| Institution: | Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | In this paper, a family of the skew elliptical distributions is defined and investigated. Some basic properties, such as stochastic representation, marginal and conditional distributions, distribution under linear transformations, moments and moment generating function are derived. The joint distribution of several quadratic forms is obtained. An example is given to show that the distributions of some statistics as the functions of the quadratic forms can be derived for various applications. |
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| Keywords: | Normal distribution Spherical distribution Skewness Moment generating function Fisher– Cochran Theorem |
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