Convex orders for linear combinations of random variables
Ma, Chunsheng
Ma, Chunsheng
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2000-03
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60E15,60K10,62G30,Arrangement increasing,Convex order,Decreasing convex order,Laplace order,Likelihood ratio order,Majorization,Reversed hazard rate order,Stochastic dominance,Stochastic order
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Chunsheng Ma, Convex orders for linear combinations of random variables, Journal of Statistical Planning and Inference, Volume 84, Issues 1–2, 2000, Pages 11-25, ISSN 0378-3758, https://doi.org/10.1016/S0378-3758(99)00143-3.
Abstract
Linear combinations ∑i=1kbiXi and ∑i=1kaiXi of random variables X1,...,Xk are ordered in the sense of the decreasing convex order and the Laplace order, where (b1,...,bk) is majorized by (a1,...,ak), when the underlying random variables are independent but possibly nonidentically distributed, and the joint density is arrangement increasing, respectively. Finite mixture distributions ∑i=1kaiFXi(x) and ∑i=1kbiFXi(x) are compared in the sense of the usual stochastic order, the convex order and higher-order stochastic dominance. The comparison between ∑i=1kIbiXi and ∑i=1kIaiXi is also studied for binary random variables Iai,Ibi(i=1,...,k). Some applications in economics and reliability are described. © 2000 Elsevier Science B.V.
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Elsevier B.V.
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Journal of Statistical Planning and Inference
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03783758