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pyvine: the Python package for regular vine copula modeling, sampling and testing. (English) Zbl 1465.62044
Summary: 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 $$\boldsymbol{E}$$ and then tests the hypothesis $$H_0^*:\boldsymbol{E}\sim C_{\perp}$$ 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.
##### MSC:
 62E17 Approximations to statistical distributions (nonasymptotic) 62H20 Measures of association (correlation, canonical correlation, etc.) 62H05 Characterization and structure theory for multivariate probability distributions; copulas 62-08 Computational methods for problems pertaining to statistics
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