Dependence properties of B-spline copulas
Dependence properties of B-spline copulas
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B 样条联结函数的相关属性
DOI：
10.1007/s13171-019-00179-y
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Donald Richards
中科院分区：
文献类型：
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作者：
Xiaoling Dou;Satoshi Kuriki;Gwo Dong Lin;Donald Richards
利用B样条函数构造了一类Copula函数，其中包括Baker分布中的伯恩斯坦Copula函数.研究了B样条Copula函数的相关范围，证明了当B样条函数的个数趋于无穷大时，B样条Copula函数的Fréchet-Hoeffding上界是存在的.由于B-样条函数是一个阶完备的弱Tchebycheff系统，在最大相关情形下，它具有任意阶的全正性，所以本文的结果推广了经典的伯恩斯坦copula的结果.此外，我们还利用第二类斯特林数导出了相应的B样条函数在右半直线上的矩的显式表达式。
We construct by using B-spline functions a class of copulas that includes the Bernstein copulas arising in Baker’s distributions. The range of correlation of the B-spline copulas is examined, and the Fréchet–Hoeffding upper bound is proved to be attained when the number of B-spline functions goes to infinity. As the B-spline functions are well-known to be an order-complete weak Tchebycheff system from which the property of total positivity of any order follows for the maximum correlation case, the results given here extend classical results for the Bernstein copulas. In addition, we derive in terms of the Stirling numbers of the second kind an explicit formula for the moments of the related B-spline functions on the right half-line.