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Why Copulas Have Been Successful in Many Practical Applications: A Theoretical Explanation Based on Computational Efficiency

机译:为什么Copulas在许多实际应用中都取得成功:基于计算效率的理论解释

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A natural way to represent a 1-D probability distribution is to store its cumulative distribution function (cdf) F(x) = Prob(X≤ x). When several random variables X_1,..., X_n are independent, the corresponding cdfs F_1(x_1),..., F_n(x_n) provide a complete description of then-joint distribution. In practice, there is usually some dependence between the variables, so, in addition to the marginals F_i(x_i), we also need to provide an additional information about the joint distribution of the given variables. It is possible to represent this joint distribution by a multi-D cdf F(x_i, ...,x_n) = Prob(X_1 ≤
机译:表示一维概率分布的自然方法是存储其累积分布函数(cdf)F(x)= Prob(X≤x)。当几个随机变量X_1,...,X_n是独立的时,相应的cdfs F_1(x_1),...,F_n(x_n)提供了当时联合分布的完整描述。实际上,变量之间通常存在一些依存关系,因此,除了边际F_i(x_i)外,我们还需要提供有关给定变量的联合分布的其他信息。可以通过多D cdf F(x_i,...,x_n)= Prob(X_1≤

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