Consistency of a Certain Class of Empirical Density Functions.
Constant rate distributions on partially ordered sets.
Constructing copulas by means of pairs of order statistics
In this paper, we introduce two transformations on a given copula to construct new and recover already-existent families. The method is based on the choice of pairs of order statistics of the marginal distributions. Properties of such transformations and their effects on the dependence and symmetry structure of a copula are studied.
Constructing infinitely divisible characteristic functions
Construction methods for gaussoids
The number of -gaussoids is shown to be a double exponential function in . The necessary bounds are achieved by studying construction methods for gaussoids that rely on prescribing -minors and encoding the resulting combinatorial constraints in a suitable transitive graph. Various special classes of gaussoids arise from restricting the allowed -minors.
Construction of multivariate copulas in -boxes
In this paper we give an alternative proof of the construction of -dimensional ordinal sums given in Mesiar and Sempi [17], we also provide a new methodology to construct -copulas extending the patchwork methodology of Durante, Saminger-Platz and Sarkoci in [6] and [7]. Finally, we use the gluing method of Siburg and Stoimenov [20] and its generalization in Mesiar et al. [15] to give an alternative method of patchwork construction of -copulas, which can be also used in composition with our patchwork...
Construction of multivariate distributions: a review of some recent results.
The construction of multivariate distributions is an active field of research in theoretical and applied statistics. In this paper some recent developments in this field are reviewed. Specifically, we study and review the following set of methods: (a) Construction of multivariate distributions based on order statistics, (b) Methods based on mixtures, (c) Conditionally specified distributions, (d) Multivariate skew distributions, (e) Distributions based on the method of the variables in common and...
Convolution property and exponential bounds for symmetric monotone densities
Our first theorem states that the convolution of two symmetric densities which are k-monotone on (0,∞) is again (symmetric) k-monotone provided 0 < k ≤ 1. We then apply this result, together with an extremality approach, to derive sharp moment and exponential bounds for distributions having such shape constrained densities.
Copula and semicopula transforms.
Copulas with given values on a horizontal and a vertical section
In this paper we study the set of copulas for which both a horizontal section and a vertical section have been given. We give a general construction for copulas of this type and we provide the lower and upper copulas with these sections. Symmetric copulas with given horizontal section are also discussed, as well as copulas defined on a grid of the unit square. Several examples are presented.
Couples de Wald indéfiniment divisibles. Exemples liés à la fonction gamma d'Euler et à la fonction zeta de Riemann
A toute mesure positive sur telle que , nous associons un couple de Wald indéfiniment divisible, i.e. un couple de variables aléatoires tel que et sont indéfiniment divisibles, , et pour tout . Plus généralement, à une mesure positive sur telle que pour tout , nous associons une “famille d’Esscher” de couples de Wald indéfiniment divisibles. Nous donnons de nombreux exemples de telles familles d’Esscher. Celles liées à la fonction gamma et à la fonction zeta de Riemann possèdent...
Decomposability of point measures in generalized convolution algebras
Décompositions d'un intervalle réel et des ensembles de Cantor
Defects and transformations of quasi-copulas
Six different functions measuring the defect of a quasi-copula, i. e., how far away it is from a copula, are discussed. This is done by means of extremal non-positive volumes of specific rectangles (in a way that a zero defect characterizes copulas). Based on these defect functions, six transformations of quasi-copulas are investigated which give rise to six different partitions of the set of all quasi-copulas. For each of these partitions, each equivalence class contains exactly one copula being...
Définition et lois de probabilité des répartitions ponctuelles aléatoires
Démonstration probabiliste d'une identité de convolution
Dependent random variables with a given marginal distribution
Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials: the discrete case.
Dispersive functions and stochastic orders
Generalizations of the hazard functions are proposed and general hazard rate orders are introduced. Some stochastic orders are defined as general ones. A unified derivation of relations between the dispersive order and some other orders of distributions is presented
Distribucion of range and quasi-range from double truncated exponential distribution.
For a doubly truncated exponential distribution, the probability density function of a quasi-range is derived. From this the density of sample range is obtained as a special case. Expressions for the mean and variance of the range are also obtained.