We investigate the properties of a new transformation of copulas based on the co-copula and an univariate function. It is shown that several families in the copula literature can be interpreted as particular outputs of this transformation. Symmetry, association, ordering and dependence properties of the resulting copula are established.
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 two companies or lines of business are related through a random common loss factor which is then multiplied by an individual random company factor to get the total loss amounts. The new two-component copula is not Archimedean and it extends the toolkit of copulas for the insurance industry.
Úbeda-Flores showed that the range of multivariate Spearman’s footrule for copulas of dimension d ≥ 2 is contained in the interval [−1/d, 1], that the upper bound is attained exclusively by the upper Fréchet-Hoeffding bound, and that the lower bound is sharp in the case where d = 2. The present paper provides characterizations of the copulas attaining the lower bound of multivariate Spearman’s footrule in terms of the copula measure but also via the copula’s diagonal section.
A novel generating mechanism for non-strict bivariate Archimedean copulas via the Lorenz curve of a non-negative random variable is proposed. Lorenz curves have been extensively studied in economics and statistics to characterize wealth inequality and tail risk. In this paper, these curves are seen as integral transforms generating increasing convex functions in the unit square. Many of the properties of these “Lorenz copulas”, from tail dependence and stochastic ordering, to their Kendall distribution function and the size of the singular part, depend on simple features of the random variable associated to the generating Lorenz curve. For instance, by selecting random variables with a lower bound at zero it is possible to create copulas with asymptotic upper tail dependence. An “alchemy” of Lorenz curves that can be used as general framework to build multiparametric families of copulas is also discussed.
Exchangeable copulas are used to model an extra-binomial variation in Bernoulli experiments with
a variable number of trials. Maximum likelihood inference procedures for the intra-cluster correlation are
constructed for several copula families. The selection of a particular model is carried out using the Akaike
information criterion (AIC). Profile likelihood confidence intervals for the intra-cluster correlation are constructed
and their performance are assessed in a simulation experiment. The sensitivity of the inference to
the specification of the copula family is also investigated through simulations. Numerical examples are presented.
This paper introduces a weighted entropic copula from preliminary knowledge of dependence. Considering a copula with common distribution we formulate the weighted entropy dependence model (WMEC). We give an approximator for the copula function of this problem. Also, we discuss some asymptotical properties regarding the unknown parameters of the model.
Wang, Li and Gupta  first introduced the skew chi-square distribution based on the multivariate skew normal distribution provided by Azzalini , and Ye, Wang and Gupta  extended this results into the skew Wishart distribution. Motivated by these results, we first study a new type of multivariate skew normal distribution introduced by Gupta and Chen , the moment generating function, independence and quadratic form are discussed, and also a new type of skew chi-square distribution was introduced. Later on, we defined a new type of skew Wishart distribution based on the matrix skew normal models introduced by Ning . In the end, we will study the probabilistic representation of multivariate skew elliptical models.
If the distribution of the linear combination of two independent and identically distributed random variables from a distribution belongs to the same distribution, then we call that distribution a stable distribution. The Levy distribution is a member of the family of stable distributions. In this paper, we will present some basic distributional properties and characterizations of the Levy distribution.
We present a constructive and self-contained approach to data driven infinite partition-of-unity copulas that were recently introduced in the literature. In particular, we consider negative binomial and Poisson copulas and present a solution to the problem of fitting such copulas to highly asymmetric data in arbitrary dimensions.