Mean residual life order of convolutions of heterogeneous exponential random variables

JOURNAL OF MULTIVARIATE ANALYSIS

卷:100

Article

Zhao, Peng¹  Balakrishnan, N.² 

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

[2] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4K1, Canada

关键词: Stochastic order;    Hazard rate order;    Likelihood ratio order;    Majorization;    Reciprocal majorization order;   

DOI  :  10.1016/j.jmva.2009.02.009

来源: Elsevier

【 摘 要 】

In this paper, we study convolutions of heterogeneous exponential random variables with respect to the mean residual life order. By introducing a new partial order (reciprocal majorization order), we prove that this order between two parameter vectors implies the mean residual life order between convolutions of two heterogeneous exponential samples. For the 2-dimensional case, it is shown that there exists a stronger equivalence. We discuss, in particular, the case when one convolution involves identically distributed variables, and show in this case that the mean residual life order is actually associated with the harmonic mean of parameters. Finally, we derive the best gamma bounds for the mean residual life function of any convolution of exponential distributions under this framework. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free