On the distribution of products of independent beta variables
On the dominance relation between ordinal sums of conjunctors
This contribution deals with the dominance relation on the class of conjunctors, containing as particular cases the subclasses of quasi-copulas, copulas and t-norms. The main results pertain to the summand-wise nature of the dominance relation, when applied to ordinal sum conjunctors, and to the relationship between the idempotent elements of two conjunctors involved in a dominance relationship. The results are illustrated on some well-known parametric families of t-norms and copulas.
On the Entropy and Inaccuracy of Similarly and Oppositely Ordered Discrete Probability Distributions (I).
On the exact distributional asymptotics for the supremum of a random walk with increments in a class of light-tailed distribution.
On the existence of exponential moments of Rademacher sums
On the Exponential Law.
On the exponentials of fractional Ornstein-Uhlenbeck processes.
On the generalization of the STER distribution applied to generalized hypergeometric parents
On the generalized logistic and log-logistic distributions
On the Heyde theorem for discrete Abelian groups
Let X be a countable discrete Abelian group, Aut(X) the set of automorphisms of X, and I(X) the set of idempotent distributions on X. Assume that α₁, α₂, β₁, β₂ ∈ Aut(X) satisfy . Let ξ₁, ξ₂ be independent random variables with values in X and distributions μ₁, μ₂. We prove that the symmetry of the conditional distribution of L₂ = β₁ξ₁ + β₂ξ₂ given L₁ = α₁ξ₁ + α₂ξ₂ implies that μ₁, μ₂ ∈ I(X) if and only if the group X contains no elements of order two. This theorem can be considered as an analogue...
On the infinite divisibility of scale mixtures of symmetric α-stable distributions, α ∈ (0,1]
The paper contains a new and elementary proof of the fact that if α ∈ (0,1] then every scale mixture of a symmetric α-stable probability measure is infinitely divisible. This property is known to be a consequence of Kelker's result for the Cauchy distribution and some nontrivial properties of completely monotone functions. It is known that this property does not hold for α = 2. The problem discussed in the paper is still open for α ∈ (1,2).
On the iteration of entire functions
On the k-gamma q-distribution
We provide combinatorial as well as probabilistic interpretations for the q-analogue of the Pochhammer k-symbol introduced by Díaz and Teruel. We introduce q-analogues of the Mellin transform in order to study the q-analogue of the k-gamma distribution.
On the Laplace Transforms of Logconcave Densities
On the Linear Combinations of Stochastic Variables.
On the Maximal Lévy-Ottaviani Inequality for Sums of Independent and Dependent Random Vectors
We prove that the sums of independent random vectors satisfy , t ≥ 0.
On the micture of some sontinuous distributions
On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
Let be the empirical distribution function (df) pertaining to independent random variables with continuous df . We investigate the minimizing point of the empirical process , where is another df which differs from . If and are locally Hölder-continuous of order at a point our main result states that converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous Poisson-process with a drift. The time-transformation...
On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
Let Fn be the empirical distribution function (df) pertaining to independent random variables with continuous df F. We investigate the minimizing point of the empirical process Fn - F0, where F0 is another df which differs from F. If F and F0 are locally Hölder-continuous of order α at a point τ our main result states that converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous Poisson-process with a drift. The time-transformation...
On the multivariate skew-normal distribution and its scale mixtures.