This paper makes two contributions. The first is to propose a new family of copulas for which the copula arguments are uncorrelated but dependent. Specifically, if w₁ and w₂ are the uniform random variables in the copula, they are uncorrelated, but w₁ is correlated with |w₂ − 1/2|. We show how this family of copulas can be applied to the error structure in an econometric production frontier model. The second contribution is to give some general results on how to extend a two-dimensional copula to three or more dimensions. This extension is necessary in our production frontier model when there are multiple inputs, but our results apply more generally to the extension of arbitrary two-dimensional copulas. We also report the results of some simulations and we give an empirical example.

本文有两个贡献。第一个是提出一个新的系动词族，其系动词论据是不相关的，但却是相互依赖的。具体而言，如果w ₁和w ₂是系数中的统一随机变量，则它们是不相关的，但w ₁与|关联。w ₂ − 1/2 |。我们展示了如何将这一系列的copulas应用于计量经济生产前沿模型中的错误结构。第二个贡献是就如何将二维copula扩展到三个或更多个维度给出一些一般性结果。当有多个输入时，这种扩展在我们的生产前沿模型中是必需的，但是我们的结果更普遍地适用于任意二维copula的扩展。我们还报告了一些模拟的结果，并给出了一个经验示例。