Distribution of linear combinations of unordered and ordered components of an elliptical random vector

作者：Mahmoodian H; Pourdarvish A; Balakrishnan N; Jamalizadeh Ahad^*

来源：Journal of the Korean Statistical Society, 2012, 41(2): 257-265.

DOI：10.1016/j.jkss.2011.09.003

• Elliptical distribution
• Multivariate unified skew-elliptical distribution
• Order statistics
• Mixture distribution
• Linear combination
• Multivariate unified skew-normal distribution
• Multivariate unified skew-t distribution

In this paper, by considering a (k + n)-dimensional random vector (X-T, Y-T)(T), X is an element of R-k and Y is an element of R-n, having a multivariate elliptical distribution, we derive the exact distribution of AX + LY(n), where A is an element of R-pxk, L is an element of R-pxn, and Y-(n) = (Y-(1), Y-(2), . . . , Y-(n))(T) denotes the vector of order statistics from Y. Next, we discuss the distribution of a(T)X + bY((r)), for r = 1, . . . , n, a = (a(1), . . . , a(k))(T) is an element of R-k and b is an element of 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.

• 出版日期2012-6