Characterizations using intersections of random events.
Characterizing the general multivariate normal distribution through the conditional distributions.
In this paper we give a characterization of the multivariate normal distribution through the conditional distributions in the most general case, which include the singular distribution.
Charges, poids et mesures de Lévy dans les espaces vectoriels localement convexes
Chevet type inequality and norms of submatrices
We prove a Chevet type inequality which gives an upper bound for the norm of an isotropic log-concave unconditional random matrix in terms of the expectation of the supremum of “symmetric exponential” processes, compared to the Gaussian ones in the Chevet inequality. This is used to give a sharp upper estimate for a quantity that controls uniformly the Euclidean operator norm of the submatrices with k rows and m columns of an isotropic log-concave unconditional random matrix. We apply these estimates...
Class of unimodal distributions and its transformations
Classes of measures closed under mixing and convolution. Weak stability
For a random vector X with a fixed distribution μ we construct a class of distributions ℳ(μ) = μ∘λ: λ ∈ , which is the class of all distributions of random vectors XΘ, where Θ is independent of X and has distribution λ. The problem is to characterize the distributions μ for which ℳ(μ) is closed under convolution. This is equivalent to the characterization of the random vectors X such that for all random variables Θ₁, Θ₂ independent of X, X’ there exists a random variable Θ independent of X such...
Commentaire de l'article : «The relevation transform and a generalization of the gamma distribution function»
Comparación de curvas de supervivencia gamma estocásticamente ordenadas.
En este trabajo se propone un análisis de supervivencia basado en un modelo Gamma. Se obtienen las condiciones teóricas bajo las cuales dos funciones de supervivencia Gamma están estocásticamente ordenadas. Estos resultados se utilizan para proponer un método sencillo que permite comparar dos poblaciones cuando, a priori, se conoce que sus curvas de supervivencia están estocásticamente ordenadas. Los resultados se ejemplifican con el análisis de un banco de datos reales sobre tiempos de desempleo....
Comparison of order statistics in a random sequence to the same statistics with I.I.D. variables
The paper is motivated by the stochastic comparison of the reliability of non-repairable -out-of- systems. The lifetime of such a system with nonidentical components is compared with the lifetime of a system with identical components. Formally the problem is as follows. Let be positive independent random variables with common distribution . For and , let consider and . Remark that this is no more than a change of scale for each term. For let us define to be the th order statistics...
Comparison of order statistics in a random sequence to the same statistics with i.i.d. variables
The paper is motivated by the stochastic comparison of the reliability of non-repairable k-out-of-n systems. The lifetime of such a system with nonidentical components is compared with the lifetime of a system with identical components. Formally the problem is as follows. Let Ui,i = 1,...,n, be positive independent random variables with common distribution F. For λi > 0 and µ > 0, let consider Xi = Ui/λi and Yi = Ui/µ, i = 1,...,n. Remark that this is no more than a change of scale for each...
Comparison theorems for small deviations of random series.
Comparison theorems of isoperimetric type for moments of compact sets.
A unified approach to prove isoperimetric inequalities for moments and basic inequalities of interpolation spaces L(p,q) is developed. Instead symmetrization methods we use a monotonicity property of special Stiltjes' means.
Comparisons between tail probabilities of sums of independent symmetric random variables
Complément sur «le support des lois indéfiniment divisibles»
Complete convergence for negatively dependent random variables.
Complete convergence of weighted sums for arrays of rowwise -mixing random variables
In this paper, we establish the complete convergence and complete moment convergence of weighted sums for arrays of rowwise -mixing random variables, and the Baum-Katz-type result for arrays of rowwise -mixing random variables. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequences of -mixing random variables is obtained. We extend and complement the corresponding results of X. J. Wang, S. H. Hu (2012).
Completely stable measures on Hilbert spaces
Componentwise concave copulas and their asymmetry
The class of componentwise concave copulas is considered, with particular emphasis on its closure under some constructions of copulas (e.g., ordinal sum) and its relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the -measure of non-exchangeability for copulas belonging to this class.
Compositional models, Bayesian models and recursive factorization models
Compositional models are used to construct probability distributions from lower-order probability distributions. On the other hand, Bayesian models are used to represent probability distributions that factorize according to acyclic digraphs. We introduce a class of models, called recursive factorization models, to represent probability distributions that recursively factorize according to sequences of sets of variables, and prove that they have the same representation power as both compositional...
Compound Poisson approximation for extremes of moving minima in arrays of independent random variables
We present conditions sufficient for the weak convergence to a compound Poisson distribution of the distributions of the kth order statistics for extremes of moving minima in arrays of independent random variables.