Monotonicity of the (reversed) hazard rate of the (maximum) minimum in bivariate distributions

被引：6

作者：

Gupta, RC ^{[1
]}

Gupta, RD

Gupta, PL

机构：

[1] Univ Maine, Dept Math & Stat, Orono, ME 04469 USA

[2] Univ New Brunswick, Dept Comp Sci & Appl Stat, St John, NB E2L 4L5, Canada

[3] Univ Maine, Dept Math & Stat, Orono, ME 04469 USA

来源：

METRIKA | 2006年 / 63卷 / 02期

关键词：

bivariate distributions; Farlie-Gumbel-Morgenstem distributions; monotonicity of the hazard rate; Sarmanov family;

D O I：

10.1007/s00184-005-0014-y

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

It is well known that in the case of independent random variables, the (reversed) hazard rate of the (maximum) minimum of two random variables is the sum of the individual (reversed) hazard rates and hence the monotonicity of the (reversed) hazard rate of the marginals is preserved by the monotonicity of the (reversed) hazard rate of the (maximum) minimum. However, for the bivariate distributions this property is not always preserved. In this paper, we study the monotonicity of the (reversed) hazard rate of the (maximum) minimum for two well known families of bivariate distributions viz the Farlie-Gumbel-Morgenstem (FGM) and Sarmanov family. In case of the FGM family, we obtain the (reversed) hazard rate of the (maximum) minimum and provide several examples in some of which the (reversed) hazard rate is monotonic and in others it is non-monotonic. In the case of Sarmanov family the (reversed) hazard rate of the (maximum) minimum

引用

页码：223 / 241

页数：19

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