Denuit, Michel
[UCL]
Mesfioui, Mhamed
[Université du Québec à Trois-Rivières (Québec), Canada]
It is known that the sums of the components of two random vectors (X1,X2,…,Xn) and (Y1,Y2,…,Yn) ordered in the multivariate (s1,s2,…,sn)-increasing convex order are ordered in the univariate (s1+s2+…+sn)-increasing convex order. More generally, real-valued functions of (X1,X2,…,Xn) and (Y1,Y2,…,Yn) are ordered in the same sense as long as these functions possess some specified non-negative cross derivatives. This note extends these results to multivariate functions. In particular, we consider vectors of partial sums (S1,S2,…,Sn) and (T1,T2,…,Tn) where Sj = X1+…+Xj and Tj = Y1 +…+Yj and we show that these random vectors are ordered in the multivariate (s1,s1+s2,…,s1+…+sn)-increasing convex order. The consequences of these general results for the upper orthant order and the orthant convex order are discussed.
- Boutsikas Michael V., Vaggelatou Eutichia, On the distance between convex-ordered random variables, with applications, 10.1239/aap/1025131222
- Denuit Michel M., Mesfioui Mhamed, Generalized increasing convex and directionally convex orders, 10.1239/jap/1269610830
- Denuit, M., Lefevre, Cl., Shaked, M.: The s-convex orders among real random variables, with applications. Math. Inequal. Appl. 1, 585–613 (1998)
- Stochastic Orders, ISBN:9780387329154, 10.1007/978-0-387-34675-5
| Bibliographic reference |
Denuit, Michel ; Mesfioui, Mhamed. Ordering Functions of Random Vectors, with Application to Partial Sums. In: Journal of Theoretical Probability, Vol. 26, no. 2, p. 474-479 (2013) |
| Permanent URL |
http://hdl.handle.net/2078.1/129536 |
