José Juan Quesada-Molina

Bivariate copulas with cubic sections

In this paper we present a method for construction families of bivariate copulas with cubic cross sections. We study dependence properties, measures of association, and concepts of symmetry for these copulas. Examples of both symmetric and asymmetric copulas with cubic sections are presented which extend some well known families of bivariate copulas (such as the iterated Farlie-Gumbel-Morgenstern, Kimeldorf and Sampson, Lin, and Sarmanov families of copulas) and which provide second-order approximations to the Frank and Plackett families of copulas.

BOUNDS ON BIVARIATE DISTRIBUTION FUNCTIONS WITH GIVEN MARGINS AND MEASURES OF ASSOCIATION

We find pointwise best-possible bounds on the bivariate distribution function of continuous random variables with given margins and a given value of the population version of a nonparametric measure of association such as Kendalls tau or Spearmans rho.

On a family of multivariate copulas for aggregation processes

We introduce a family of multivariate copulas - a special type of n-ary aggregation operations - depending on a univariate function. This family is used in the construction of a special aggregation operation that satisfies a Lipschitz condition. Several examples are provided and some statistical properties are studied.

Some New Properties of Quasi-Copulas

Abstract The notion of a quasi-copula was introduced by Alsina et al. (1993) to characterize operations on distribution functions that can or cannot be derived from operations on random variables. Genest et al. (1999) characterize the quasi-copula concept in simpler operational terms. We present a new simple characterization and some properties of these functions, all of them concerning the mass distribution of a quasi-copula. We show that the features of this mass distribution can be quite different from that of a copula.

Some advances in the study of the compatibility of three bivariate copulas

In this paper we study the problem of the compatibility of three bivariate copulas, i.e., we look for conditions which allow us to assure the existence of a three-copula whose two-dimensional margins are given. As a particular case, we seek conditions for two bivariate copulasC 1 andC 2 under whichC 2[C1 (x, y), z] is a three-copula. We specifically study the compatibility of the copulasM, W andII with other copulas both in general and in the particular case. We also study the compatibility of a two-copula with convex linear combinations of other two-copulas. Several examples illustrate the results obtained in each case, and some applications are given.

A generalization of an identity of hoeffding and some applications

We generalize a well-known identity due to Hoeffding and use this generalization to prove a result of Cambanis, Simons and Stout under somewhat different hypotheses and to extend some results of Lehmann concerning bivariate distributions with quadrant dependence.

Bounds for Trivariate Copulas with Given Bivariate Marginals

We determine under which conditions three bivariate copulas C12, C13 and C23 are compatible, viz. they are the bivariate marginals of the same trivariate copula C̃, and, then, construct the class of these copulas. In particular, the upper and lower bounds for this class of trivariate copulas are determined.We determine two constructions that, starting with two bivariate copulas, give rise to new bivariate and trivariate copulas, respectively. These constructions are used to determine pointwise upper and lower bounds for the class of all trivariate copulas with given bivariate marginals.

Quasi-copulas and signed measures

We study the relationship between multivariate quasi-copulas and measures that they may or may not induce on [0,1]^n. We first study the mass distribution of the pointwise best possible lower bound for the set of n-quasi-copulas for n>=3. As a consequence, we show that not every n-quasi-copula induces a signed measure on [0,1]^n.

Multivariate Archimedean Quasi-Copulas

Abstract In this paper we define and study basic properties of multivariate Archimedean quasi-copulas. In particular, we examine properties concerning generators, diagonal sections, permutation symmetry, level sets and order.

On the α-migrativity of multivariate semi-copulas

In this paper we introduce and study the @a-migrative property for the class of multivariate semi-copulas. In particular, a characterization of @a-migrative copulas is provided.