Related papers: New copulas based on general partitions-of-unity a…
We present a constructive and self-contained approach to data driven general partition-of-unity copulas that were recently introduced in the literature. In particular, we consider Bernstein-, negative binomial and Poisson copulas and…
We construct new multivariate copulas on the basis of a generalized infinite partition-of-unity approach. This approach allows - in contrast to finite partition-of-unity copulas - for tail-dependence as well as for asymmetry. A possibility…
In this paper we discuss a natural extension of infinite discrete partition-of-unity copulas which were recently introduced in the literature to continuous partition of copulas with possible applications in risk management and other fields.…
This paper presents a new copula to model dependencies between insurance entities, by considering how insurance entities are affected by both macro and micro factors. The model used to build the copula assumes that the insurance losses of…
Zero-inflated continuous data ubiquitously appear in many fields, in which lots of exactly zero-valued data are observed while others distribute continuously. Due to the mixed structure of discreteness and continuity in its distribution,…
A new class of copulas based on order statistics was introduced by Baker (2008). Here, further properties of the bivariate and multivariate copulas are described, such as that of likelihood ratio dominance (LRD), and further bivariate…
A new method for constructing absolutely continuous two--dimensional copulas by differential equations is presented. The copulas are symmetric with respect to reflection in the opposite diagonal. The support of the copula density may be…
This paper proposes a new generalized linear model with the fractional binomial distribution. Zero-inflated Poisson/negative binomial distributions are used for count data with many zeros. To analyze the association of such a count variable…
We offer a new perspective on risk aggregation with FGM copulas. Along the way, we discover new results and revisit existing ones, providing simpler formulas than one can find in the existing literature. This paper builds on two novel…
We consider the integration of two-dimensional, piecewise constant functions with respect to copulas. By drawing a connection to linear assignment problems, we can give optimal upper and lower bounds for such integrals and construct the…
Using the notion of a contravariant derivative, we give some algebraic and geometric characterizations of Poisson algebras associated to the infinitesimal data of Poisson submanifolds. We show that such a class of Poisson algebras provides…
For continuous boundary data, including data of polynomial growth, modified Poisson integrals are used to write solutions to the half space Dirichlet and Neumann problems in $\mathbb{R}^{n}$. Pointwise growth estimates for these integrals…
Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical…
Copulas, generalized estimating equations, and generalized linear mixed models promote the analysis of grouped data where non-normal responses are correlated. Unfortunately, parameter estimation remains challenging in these three…
We present a constructive approach to Bernstein copulas with an admissible discrete skeleton in arbitrary dimensions when the underlying marginal grid sizes are smaller than the number of observations. This prevents an overfitting of the…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset…
We present a joint copula-based model for insurance claims and sizes. It uses bivariate copulae to accommodate for the dependence between these quantities. We derive the general distribution of the policy loss without the restrictive…
New copulas, based on perturbation theory, are introduced to clarify a \emph{symmetrization} procedure for asymmetric copulas. We give also some properties of the \emph{symmetrized} copula. Finally, we examine families of copulas with a…
The decreasing enumeration of the points of a Poisson random measure whose mean measure has finite survival function on the positive half-axis can be represented as a non-increasing function of the jump times of a standard Poisson process.…
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…