Tail-thickness in terms of COV(Xj2,Xp2) in the class of elliptical distributions

✍ Scribed by Jiro Hodoshima

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 178 KB
• Volume: 121
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(03)00118-6

✦ Synopsis

In this note, we present a new classiÿcation of tail-thickness in terms of COV(X 2 j ; X 2 p ) in the class of elliptical distributions. The tail-thickness measured by the sign of the kurtosis parameter is shown to be equivalent to the sign of COV(X 2 j ; X 2 p ) when COV(Xj; Xp) = 0. When COV(Xj; Xp) = 0, if E(Xj) = 0 or E(Xp) = 0, the tail-thickness is shown to be equivalent to the sign of a corrected version of COV(X 2 j ; X 2 p ), i.e., COV(X 2 j ; X 2 p ) -2 COV 2 (Xj; Xp). The results are based on an expression for covariances of the form COV(XjX k ; X 2 p ) with j; k = p.