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Ahad Jamalizadeh,H. Mahmoodian,A. Pourdarvish,N. Balakrishnan 한국통계학회 2012 Journal of the Korean Statistical Society Vol.41 No.2
In this paper, by considering a (k + n)-dimensional random vector XT , YT T , X ∈ Rk and Y ∈ Rn, having a multivariate elliptical distribution, we derive the exact distribution of AX + LY (n), where A ∈ Rp×k, L ∈ Rp×n, and Y(n) = Y(1), Y(2), . . . , Y(n)T denotes the vector of order statistics from Y. Next, we discuss the distribution of aTX+bY(r), for r = 1, . . . ,n, a =(a1, . . . , ak)T ∈ Rk and b ∈ R. We show that these distributions can be expressed as mixtures of multivariate unified skew-elliptical distributions. Finally, we illustrate an application of the established results to stock fund evaluation.