Regular vine copula provides rich models for dependence structure modeling. It combines vine structures and families of bivariate copulas to construct a number of multivariate distributions that can model a wide range dependence patterns with different tail dependence for different pairs. Two special cases of regular vine copulas, C-vine and D-vine copulas, have been extensively investigated in the literature. We propose the Python package, pyvine, for modeling, sampling and testing a more generalized regular vine copula (R-vine for short). R-vine modeling algorithm searches for the R-vine structure which maximizes the vine tree dependence in a sequential way. The maximum likelihood estimation algorithm takes the sequential estimations as initial values and uses L-BFGS-B algorithm for the likelihood value optimization. R-vine sampling algorithm traverses all edges of the vine structure from the last tree in a recursive way and generates the marginal samples on each edge according to some nested conditions. Goodness-of-fit testing algorithm first generates Rosenblatt’s transformed data \({\varvec{E}}\) and then tests the hypothesis \(H_0^*: {\varvec{E}} \sim C_{\perp }\) by using Anderson–Darling statistic, where \(C_{\perp }\) is the independence copula. Bootstrap method is used to compute an adjusted p-value of the empirical distribution of replications of Anderson–Darling statistic. The computing of related functions of copulas such as cumulative distribution functions, H-functions and inverse H-functions often meets with the problem of overflow. We solve this problem by reinvestigating the following six families of bivariate copulas: Normal, Student t, Clayton, Gumbel, Frank and Joe’s copulas. Approximations of the above related functions of copulas are given when the overflow occurs in the computation. All these are implemented in a subpackage bvcopula, in which subroutines are written in Fortran and wrapped into Python and, hence, good performance is guaranteed.

常规藤蔓copula为依赖结构建模提供了丰富的模型。它结合了藤本植物的结构和二元系系的家族，构建了许多多元分布，可以为不同的成对模型建立广泛的尾巴依存关系。在文献中已经广泛研究了两种常规的葡萄藤蔓小例，C-葡萄藤蔓和D-葡萄藤蔓小蔓。我们建议使用python软件包pyvine，用于建模，采样和测试更通用的常规藤蔓copula（简称R-vine）。R-vine建模算法搜索R-vine结构，该结构以顺序方式最大化藤蔓树的依赖性。最大似然估计算法将顺序估计作为初始值，并使用L-BFGS-B算法进行似然值优化。R-vine采样算法以递归方式遍历最后一棵树的所有藤蔓结构边缘，并根据一些嵌套条件在每个边缘上生成边际样本。拟合优度测试算法首先生成Rosenblatt的变换数据\ {{\ varvec {E}} \}，然后测试假设\ {H_0 ^ *：{\ varvec {E}} \ sim C _ {\ perp} \）通过使用Anderson-Darling统计信息，其中\（C _ {\ perp} \）是独立关联词。Bootstrap方法用于计算Anderson-Darling统计量的重复经验分布的调整后的p值。算子的相关函数如累积分布函数，H函数和反H函数的计算通常会遇到溢出问题。我们通过重新调查以下六个双变量系动词来解决此问题：正常，学生t，克莱顿，古姆贝尔，弗兰克和乔的系动词。当计算中发生溢出时，给出了关联函数的上述相关函数的近似值。所有这些都在bvcopula子包中实现，其中子例程用Fortran编写并包装到Python，并因此保证了良好的性能。