Local dependence functions for some families of bivariate distributions and total positivity
Local dependence functions for some families of bivariate distributions and total positivity
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一些二元分布族和总正性的局部依赖函数
DOI：
10.1016/j.amc.2010.02.019
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
H. Srivastava
中科院分区：
文献类型：
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作者：
Ramesh C. Gupta;S. Kirmani;H. Srivastava
本文的目的是研究Holland和Wang [20]最近考虑的局部相关函数γf（x，y）的一个非常有用的应用。γf（x，y）的一个有趣的性质是，基本的联合密度f（x，y）是TP 2（即2阶全正）当且仅当γf（x，y）≥ 0。这给出了一个优雅的方法来研究任何二元分布的TP 2性质。对于Saramanov族，Ali-Mikhail-Haq族的二元分布和二元椭圆分布族，我们导出了局部依赖函数，得到了f（x，y）为TP 2的条件.这些族是相当丰富的，包括许多其他大类的二元分布作为其特殊情况。对于具有指数条件的二元分布和具有Pareto条件的二元分布，也得到了类似的条件。
The purpose of this paper is to investigate a very useful application of a certain local dependence function γf(x,y), which was considered recently by Holland and Wang [20]. An interesting property of γf(x,y) is that the underlying joint density f(x,y) is TP2(that is, totally positive of order 2) if and only if γf(x,y)≧0. This gives an elegant way to investigate the TP2property of any bivariate distribution. For the Saramanov family, the Ali–Mikhail–Haq family of bivariate distributions and the family of bivariate elliptical distributions, we derive the local dependence function and obtain conditions for f(x,y) to be TP2. These families are quite rich and include many other large classes of bivariate distributions as their special cases. Similar conditions are obtained for bivariate distributions with exponential conditionals and bivariate distributions with Pareto conditionals.