On hazard rate ordering of the sums of heterogeneous geometric random variables

JOURNAL OF MULTIVARIATE ANALYSIS

卷:101

Article

Zhao, Peng¹  Hu, Taizhong² 

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

[2] Univ Sci & Technol China, Dept Stat & Finance, Hefei 230026, Anhui, Peoples R China

关键词: Stochastic order;    Hazard rate order;    Likelihood ratio order;    Majorization;    p-larger order;    Negative binomial;   

DOI  :  10.1016/j.jmva.2009.04.002

来源: Elsevier

【 摘 要 】

In this paper, we treat convolutions of heterogeneous geometric random variables with respect to the p-larger order and the hazard rate order. It is shown that the p-larger order between two parameter vectors implies the hazard rate order between convolutions of two heterogeneous geometric sequences. Specially in the two-dimensional case, we present ail equivalent characterization. The case when one Convolution involves identically distributed variables is discussed, and we reveal the link between the hazard rate order of convolutions and the geometric mean of parameters. Finally, we drive the best negative binomial bounds for the hazard rate function of any convolution of geometric sequence under this setup. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free