Abstract We characterize absolutely continuous symmetric copulas with square integrable densities in this paper. This characterization is used to create new copula families, that are perturbations of ...the independence copula. The full study of mixing properties of Markov chains generated by these copula families is conducted. An extension that includes the Farlie–Gumbel–Morgenstern family of copulas is proposed. We propose some examples of copulas that generate non-mixing Markov chains, but whose convex combinations generate $$\psi $$ ψ -mixing Markov chains. Some general results on $$\psi $$ ψ -mixing are given. The Spearman’s correlation $$\rho _S$$ ρ S and Kendall’s $$\tau $$ τ are provided for the created copula families. Some general remarks are provided for $$\rho _S$$ ρ S and $$\tau $$ τ . A central limit theorem is provided for parameter estimators in one example. A simulation study is conducted to support derived asymptotic distributions for some examples.
Schur-concave copulas, a distinct subclass of copulas, have emerged as a crucial component in recent advancements of copula theory. In this paper, we employ techniques from infinite-dimensional ...topology to investigate the topological structure of the space of all Schur-concave copulas equipped with the uniform metric and its topological position in the (symmetric) copula space. Moreover, we show that there exists a homeomorphism from the copula space onto the Hilbert cube, which relates the symmetric copula space onto an end of the Hilbert cube and relates the Schur-concave copula space onto an end of the end of the Hilbert cube. As a consequence, the Schur-concave copula space has the fixed point property. Furthermore, we show that a subset of the family of all associative copulas is a Z-set in the Schur-concave copula space if and only if it is compact.
In this study, a D-vine copulas modelling based probabilistic load flow (PLF) computation method is proposed, which considers the dependence among multiple wind generators. Furthermore, this method ...is not restricted by the type of wind speed distribution, i.e. allow random variables to comply with any types of distribution model. Copula theory plays an important role on dependency modelling. However, when high-dimensional correlation is taken into account, standard multivariate copula suffers from the problems of inflexible structure. Vine copula is flexible to build high-dimensional dependence and able to construct complicated dependence structure by applying bivariate copulas. For marginal distributions of wind speed, non-parametric model can provide a better estimation than those parametric models. An improved Latin hypercube sampling based Monte Carlo simulation method is utilised to solve PLF problems. A modified IEEE 33-node distribution system is used to conduct the numerical experiments for the accuracy and efficiency verification of the proposed PLF method, under the MatlabR2016a platform. The simulation results verify the outstanding accuracy, efficiency and robustness of the proposed PLF method.
This paper aims to propose a novel multi‐attribute group decision‐making (MAGDM) method based on linguistic Pythagorean fuzzy copula extended power average operator. Existing researches under ...linguistic Pythagorean fuzzy environment lack of the ability to handle with extreme values and the flexible operational rules. To fill these two gaps, this paper first provides the definition of Archimedean copula and co‐copula operational rules under linguistic Pythagorean fuzzy environment, which can reflect the connection among arguments and provide more choices for experts to express their preferences. Then, we gather the extended power average (EPA) operator to present some new aggregation operators, which can reduce the negative influence of extreme evaluation values. To show the application of the proposed method to MAGDM problems, we apply it to handle a case of takeout O2O platform assessment problem. The numerical case and comparative analysis with other existing methods illustrate that our proposed method is more scientific and flexible.
Abstract
Discovering, comparing, and contrasting natural kinds is critical for scientific progress. It should be the goal
of linguistic inquiry to seek out natural kinds within and between languages. ...Unfortunately, the most common definition of a
copula is consistently inadequate for categorizing and comparing the data in cross-linguistic research on this topic. The
categories of pseudo-copula and semi-copula have been offered to account for constructions which resemble the copular relationship
between subject and complement, though with added meaning in that relationship. I will argue that copulas, defined more broadly,
function in diverse ways cross-linguistically to instantiate the alterable feature-driven relationship between subject and
complement. This article presents a gradient view of copulas based on a set of binary featural parameters with which a language
may represent with one or more copulas. A formal description of this phenomena is also offered within in the framework of
Distributed Morphology, building on
Wilson (2020)
.
The high power consumption of Bitcoin transactions has raised environmental and sustainable concerns of green investors and regulatory bodies. We utilize the time-varying optimal copula (TVOC) ...approach to showcase the dependence structure between bitcoin and green financial assets. We find multiple tail-dependence regimes characterize the extreme dependence between bitcoin and green financial assets, and the dependence structure is mainly asymmetric and time-varying. Finally, the hedging effectiveness of green financial assets for bitcoin revealed that all green assets, especially clean energy, are effective hedges for bitcoin.
•We estimated the tail-dependence between bitcoin and green financial assets.•The time-varying optimal copula (TVOC) approach is employed on the dataset.•Tail-dependence regimes portray the extreme dependence between bitcoin and green financial assets.•Dependence structure is mainly asymmetric and time-varying.•Clean energy is valuable hedge for bitcoin.
Vector copulas Fan, Yanqin; Henry, Marc
Journal of econometrics,
05/2023, Volume:
234, Issue:
1
Journal Article
Peer reviewed
This paper introduces vector copulas associated with multivariate distributions with given multivariate marginals, based on the theory of measure transportation, and establishes a vector version of ...Sklar’s theorem. The latter provides a theoretical justification for the use of vector copulas to characterize nonlinear or rank dependence between a finite number of random vectors (robust to within vector dependence), and to construct multivariate distributions with any given non-overlapping multivariate marginals. We construct Elliptical and Kendall families of vector copulas, derive their densities, and present algorithms to generate data from them. The use of vector copulas is illustrated with a stylized analysis of international financial contagion.
The t Copula and Related Copulas Demarta, Stefano; McNeil, Alexander J.
International statistical review,
April 2005, Volume:
73, Issue:
1
Journal Article
Peer reviewed
The t copula and its properties are described with a focus on issues related to the dependence of extreme values. The Gaussian mixture representation of a multivariate t distribution is used as a ...starting point to construct two new copulas, the skewed t copula and the grouped t copula, which allow more heterogeneity in the modelling of dependent observations. Extreme value considerations are used to derive two further new copulas: the t extreme value copula is the limiting copula of componentwise maxima of t distributed random vectors; the t lower tail copula is the limiting copula of bivariate observations from a t distribution that are conditioned to lie below some joint threshold that is progressively lowered. Both these copulas may be approximated for practical purposes by simpler, better-known copulas, these being the Gumbel and Clayton copulas respectively. /// Dans cet article on décrit les propriétés de la copule t, avec particulière attention envers la dépendance des valeurs extrêmes. Exploitant la représentation de la loi multivariée t par un mélange de Gaussiennes, on construit deux nouveaux types de copule: une version biaisée (skewed t copula) et une version permettant une majeure hétérogénéité dans la modélisation des observations dépendantes (grouped t copula). Deux autres types de copule sont ensuite construits à l'aide de la théorie des valeurs extrêmes. L'une est la copule limite de la loi des maxima de chaque composante d'un vecteur aléatoire avec distribution t (t extreme value copula), l'autre est la copule limite des observations d'un vecteur bivarié obéissant à une loi t, conditionnées a être en dessous d'un certain seuil commun, qu'on baisse progressivement (t lower tail copula). En ce qui concerne les applications pratiques, ces deux dernières copules peuvent être approximées par d'autres copules plus simples et connues, comme celle de Gumbel et celle de Clayton.
In the present study, a method based on the conditional density of vine copulas was used to drought monitoring and predicting the rainfall deficiency signature for a 60‐day duration in Dashband, ...sub‐basin of Lake Urmia basin. The annual rainfall and rainfall deficiency signatures at 10‐, 30‐ and 60‐day durations were considered as variables. D‐, C‐ and R‐vine copulas were used to represent the dependence among the variables, finding that D‐vine copula results to be more accurate for the case of interest. We found that, if the rainfall is less than the long‐term mean in the region, the rainfall deficiency signature for near future can be estimated by acceptable accuracy. Moreover, the results of the conditional probability analysis of rainfall deficiency signature for a 60‐day duration respect to the other variables showed that, on average, the probability of the occurrence of rainfall deficiency signature of 250 mm compared to the long‐term mean in the study area is more than 50% per year. The results showed that the proposed approach may facilitate the meteorological drought management in the considered sub‐basin.
A 4‐D method due to the conditional density of vine copulas was proposed to provide predictive equations and simulate the values of rainfall deficiency signatures for meteorological drought management. The diagonal section of copulas was used to reduce the complexity of the conditional density of pairwise variables. While, examining the accuracy of C‐, D‐, and R‐vine copulas, the proposed method was used to predict short‐term rainfall deficiency signatures in the studied basin.
Copulas
for which
are called
copulas, of which well-studied examples are idempotent copulas and complete dependence copulas. As such, we shall work mainly with the topology induced by the modified ...Sobolev norm, with respect to which the class
of pre-idempotent copulas is closed and the class of factorizable copulas is a dense subset of
. Identifying copulas with Markov operators on
, the one-to-one correspondence between pre-idempotent copulas and partial isometries is one of our main tools. In the same spirit as Darsow and Olsen’s work on idempotent copulas, we obtain an explicit characterization of pre-idempotent copulas, which is split into cases according to the atomicity of its associated
-algebras, where the nonatomic case gives all factorizable copulas and the totally atomic case yields conjugates of ordinal sums of copies of the product copula.
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