Characterization of normality within the class of elliptical contoured distributions

C. G. Khatri and Rahul Mukerjee

Statistics & Probability Letters, 1987, vol. 5, issue 3, 187-190

Abstract: The random vector x is said to have an elliptical contoured distribution provided its characteristic function (c.f.) is exp([radical sign]- 1 t'[mu]) [phi] (t' [Sigma]t) for all t [epsilon] Rp, where [mu] [epsilon] Rp and [Sigma] is positive semi-definite. When [mu] = 0 and [Sigma] = I, the necessary and sufficient conditions are established for a quadratic form x'Ax to be distributed as chi-square. This result is extended when [mu] [not equal to] 0 and [Sigma] [not equal to] I. These conditions indicate that x must be distributed as normal.

Keywords: elliptical; contoured; distributions; quadratic; form; chi; square (search for similar items in EconPapers)
Date: 1987
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Citations: View citations in EconPapers (2)

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