Related papers: New copulas based on general partitions-of-unity (…
Being the limits of copulas of componentwise maxima in independent random samples, extreme-value copulas can be considered to provide appropriate models for the dependence structure between rare events. Extreme-value copulas not only arise…
In this paper, we use a simple discrete dynamical model to study integer partitions and their lattice. The set of reachable configurations of the model, with the order induced by the transition rule defined on it, is the lattice of all…
A class of random discrete distributions $P$ is introduced by means of a recursive splitting of unity. Assuming supercritical branching, we show that for partitions induced by sampling from such $P$ a power growth of the number of blocks is…
This paper introduces an innovative method for constructing copula models capable of describing arbitrary non-monotone dependence structures. The proposed method enables the creation of such copulas in parametric form, thus allowing the…
In a previous paper: A. Paszkiewicz, T. Sobieszek, Additive Entropies of Partitions, we have given a description of additive partition entropies that is real functions $I$ on the set of finite partitions that are additive on stochastically…
Multivariate distributions are fundamental to modeling. Discrete copulas can be used to construct diverse multivariate joint distributions over random variables from estimated univariate marginals. The space of discrete copulas admits a…
W-transforms are introduced as uniformity-preserving univariate transformations on the unit interval induced by distribution functions and piecewise strictly monotone functions, and their properties are investigated. When applied…
Several collective risk models have recently been proposed by relaxing the widely used but controversial assumption of independence between claim frequency and severity. Approaches include the bivariate copula model, random effect model,…
For multivariate distributions in the domain of attraction of a max-stable distribution, the tail copula and the stable tail dependence function are equivalent ways to capture the dependence in the upper tail. The empirical versions of…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
The continuous extension of a discrete random variable is amongst the computational methods used for estimation of multivariate normal copula-based models with discrete margins. Its advantage is that the likelihood can be derived…
Modeling of high order multivariate probability distribution is a difficult problem which occurs in many fields. Copula approach is a good choice for this purpose, but the curse of dimensionality still remains a problem. In this paper we…
A new class of copulas, termed the MGL copula class, is introduced. The new copula originates from extracting the dependence function of the multivariate generalized log-Moyal-gamma distribution whose marginals follow the univariate…
The majority of finite mixture models suffer from not allowing asymmetric tail dependencies within components and not capturing non-elliptical clusters in clustering applications. Since vine copulas are very flexible in capturing these…
For the problem of estimating lower tail and upper tail copulas, we propose two bootstrap procedures for approximating the distribution of the corresponding empirical tail copulas. The first method uses a multiplier bootstrap of the…
We introduce a novel perspective by linking ordered probabilistic choice to copula theory, a mathematical framework for modeling dependencies in multivariate distributions. Each representation of ordered probabilistic choice behavior can be…
This article proposes a space-efficient approximation to empirical tail dependence coefficients of an indefinite bivariate stream of data. The approximation, which has stream-length invariant error bounds, utilises recent work on the…
Risk measures like Marginal Expected Shortfall and Marginal Mean Excess quantify conditional risk and in particular, aid in the understanding of systemic risk. In many such scenarios, models exhibiting heavy tails in the margins and…
We introduce new estimates and tests of independence in copula models with unknown margins using $\phi$-divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the…
So far, one-factor copulas induce conditional independence with respect to a latent factor. In this paper, we extend one-factor copulas to conditionally dependent models. This is achieved through new representations which allow to build new…