78 research outputs found
Nested Archimedean Copulas Meet R: The nacopula Package
The package nacopula provides procedures for constructing nested Archimedean copulas in any dimensions and with any kind of nesting structure, generating vectors of random variates from the constructed objects, computing function values and probabilities of falling into hypercubes, as well as evaluation of characteristics such as Kendall's tau and the tail-dependence coefficients. As by-products, algorithms for various distributions, including exponentially tilted stable and Sibuya distributions, are implemented. Detailed examples are given.
Quasi-random numbers for copula models
The present work addresses the question how sampling algorithms for commonly
applied copula models can be adapted to account for quasi-random numbers.
Besides sampling methods such as the conditional distribution method (based on
a one-to-one transformation), it is also shown that typically faster sampling
methods (based on stochastic representations) can be used to improve upon
classical Monte Carlo methods when pseudo-random number generators are replaced
by quasi-random number generators. This opens the door to quasi-random numbers
for models well beyond independent margins or the multivariate normal
distribution. Detailed examples (in the context of finance and insurance),
illustrations and simulations are given and software has been developed and
provided in the R packages copula and qrng
On structure, family and parameter estimation of hierarchical Archimedean copulas
Research on structure determination and parameter estimation of hierarchical
Archimedean copulas (HACs) has so far mostly focused on the case in which all
appearing Archimedean copulas belong to the same Archimedean family. The
present work addresses this issue and proposes a new approach for estimating
HACs that involve different Archimedean families. It is based on employing
goodness-of-fit test statistics directly into HAC estimation. The approach is
summarized in a simple algorithm, its theoretical justification is given and
its applicability is illustrated by several experiments, which include
estimation of HACs involving up to five different Archimedean families.Comment: 63 pages, one attachment in attachment.pd
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