Boundedly Complete Families Which are Not Complete.
Bounds for distribution functions of sums of squares and radial errors.
Bounds of general Fréchet classes
This paper deals with conditions of compatibility of a system of copulas and with bounds of general Fréchet classes. Algebraic search for the bounds is interpreted as a solution to a linear system of Diophantine equations. Classical analytical specification of the bounds is described.
Certain infinitely divisible characteristic functions
Characteristic properties of generalized order statistics from exponential distributions
Exponential distributions are characterized by distributional properties of generalized order statistics. These characterizations include known results for ordinary order statistics and record values as particular cases.
Characterization of distributions with the length-bias scaling property.
Characterization of probability distributions by Poincaré-type inequalities
Characterizations of some Distributions Connected Wtth Extremal-type Distributions
Characterizations of the exponential distribution based on certain properties of its characteristic function
Two characterizations of the exponential distribution among distributions with support the nonnegative real axis are presented. The characterizations are based on certain properties of the characteristic function of the exponential random variable. Counterexamples concerning more general possible versions of the characterizations are given.
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.
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»
Complément sur «le support des lois indéfiniment divisibles»
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.
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.
Concentration of measure on product spaces with applications to Markov processes
For a stochastic process with state space some Polish space, this paper gives sufficient conditions on the initial and conditional distributions for the joint law to satisfy Gaussian concentration inequalities and transportation inequalities. In the case of the Euclidean space , there are sufficient conditions for the joint law to satisfy a logarithmic Sobolev inequality. In several cases, the constants obtained are of optimal order of growth with respect to the number of random variables, or are...
Conditions for bimodality and multimodality of a mixture of two unimodal densities
Conditions for bimodality of mixtures of two unimodal distributions are investigated in some special cases. Based on general characterizations, explicit criteria for the parameters are derived for mixtures of two Cauchy, logistic, Student, gamma, log-normal, Gumbel and other distributions.
Conjugate transforms and limit theorems for semigroups