Journal Article10.1080/00949650701255834
Sampling nested Archimedean copulas
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TL;DR: Algorithm for sampling from non-exchangeable Archimedean copulas created by the nesting of Archimingean copula generators, where in the most general algorithm the generators may be nested to an arbitrary depth using Laplace transforms.
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Abstract: We give algorithms for sampling from non-exchangeable Archimedean copulas created by the nesting of Archimedean copula generators, where in the most general algorithm the generators may be nested to an arbitrary depth. These algorithms are based on mixture representations of these copulas using Laplace transforms. While in principle the approach applies to all nested Archimedean copulas, in practice the approach is restricted to certain cases where we are able to sample distributions with given Laplace transforms. Precise instructions are given for the case when all generators are taken from the Gumbel parametric family or the Clayton family; the Gumbel case in particular proves very easy to simulate.
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Citations
Pair-copula constructions of multiple dependence
TL;DR: This work uses the pair-copula decomposition of a general multivariate distribution and proposes a method for performing inference, which represents the first step towards the development of an unsupervised algorithm that explores the space of possible pair-Copula models, that also can be applied to huge data sets automatically.
Multivariate Archimedean copulas, $d$-monotone functions and $\ell_1$-norm symmetric distributions
TL;DR: It is shown that a necessary and sufficient condition for an Archimedean copula generator to generate a $d-dimensional copula is that the generator is a d-monotone function.
682
Multivariate Archimedean copulas, d-monotone functions and ℓ1-norm symmetric distributions
TL;DR: In this paper, it was shown that a necessary and sufficient condition for an Archimedean copula generator to generate a d-dimensional copula is that the generator is a monotone function.
Sampling Archimedean copulas
TL;DR: The challenge of efficiently sampling exchangeable and nested Archimedean copulas is addressed, with specific focus on large dimensions, where methods involving generator derivatives are not applicable.
255
Bayesian inference for multivariate copulas using pair-copula constructions.
Aleksey Min,Claudia Czado +1 more
TL;DR: A Markov chain Monte Carlo (MCMC) algorithm is developed which allows for interval estimation by means of credible intervals and can reveal unconditional as well as conditional independence in the data which can simplify resulting PCCfs.
225
References
An introduction to probability theory and its applications - 3/E. volume 3
William Feller
- 22 Mar 2002
Abstract: The classic text for understanding complex statistical probability An Introduction to Probability Theory and Its Applications offers comprehensive explanations to complex statistical problems. Delving deep into densities and distributions while relating critical formulas, processes and approaches, this rigorous text provides a solid grounding in probability with practice problems throughout. Heavy on application without sacrificing theory, the discussion takes the time to explain difficult topics and how to use them. This new second edition includes new material related to the substitution of probabilistic arguments for combinatorial artifices as well as new sections on branching processes, Markov chains, and the DeMoivreLaplace theorem.
21.5K
An Introduction To Probability Theory And Its Applications
Feller William
- 01 Jan 1950
TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
10.2K
•Book
An Introduction to Copulas
Roger B. Nelsen
- 01 Jan 1999
TL;DR: This book discusses the fundamental properties of copulas and some of their primary applications, which include the study of dependence and measures of association, and the construction of families of bivariate distributions.
8.7K