On the Unimodality and self-Decomposability of Certain Transformed Distributions
On the Unimodality of Discrete Probability Measures.
On the Urysohn condition and the convergence of probability distributions
On the zeroes of some random functions
On Three and Five Parameter Bivariate Beta Distributions.
On two functional equations connected with the characterizations of the distance measures.
On uniform tail expansions of multivariate copulas and wide convergence of measures
The theory of copulas provides a useful tool for modeling dependence in risk management. In insurance and finance, as well as in other applications, dependence of extreme events is particularly important, hence there is a need for a detailed study of the tail behaviour of multivariate copulas. We investigate the class of copulas having regular tails with a uniform expansion. We present several equivalent characterizations of uniform tail expansions. Next, basing on them, we determine the class of...
On univariate and bivariate aging for dependent lifetimes with Archimedean survival copulas
Let be a pair of exchangeable lifetimes whose dependence structure is described by an Archimedean survival copula, and let denotes the corresponding pair of residual lifetimes after time , with . This note deals with stochastic comparisons between and : we provide sufficient conditions for their comparison in usual stochastic and lower orthant orders. Some of the results and examples presented here are quite unexpected, since they show that there is not a direct correspondence between univariate...
On Urbanik's characterization of Gaussian measures on locally compact abelian groups
On Weak Tail Domination of Random Vectors
Motivated by a question of Krzysztof Oleszkiewicz we study a notion of weak tail domination of random vectors. We show that if the dominating random variable is sufficiently regular then weak tail domination implies strong tail domination. In particular, a positive answer to Oleszkiewicz's question would follow from the so-called Bernoulli conjecture. We also prove that any unconditional logarithmically concave distribution is strongly dominated by a product symmetric exponential measure.
On Wiener–Hopf factors for stable processes
We give a series representation of the logarithm of the bivariate Laplace exponent κ of α-stable processes for almost all α ∈ (0, 2].
Open problems posed at the tenth International conference on fuzzy set theory and applications (FSTA 2010, Liptovský Ján, Slovakia)
Eighteen open problems posed during FSTA 2010 (Liptovský Ján, Slovakia) are presented. These problems concern copulas, triangular norms and related aggregation functions. Some open problems concerning effect algebras are also included.
Opérateurs réguliers sur les espaces
Operations on distribution functions not derivable from operations on random variables
Operator semistable probability measures on Banach spaces
Operator semistable probability measures on
Operator-stable probability measures on Banach spaces
Optimal mean-variance bounds on order statistics from families determined by star ordering
We present optimal upper bounds for expectations of order statistics from i.i.d. samples with a common distribution function belonging to the restricted family of probability measures that either precede or follow a given one in the star ordering. The bounds for families with monotone failure density and rate on the average are specified. The results are obtained by projecting functions onto convex cones of Hilbert spaces.
Optimal nonlinear transformations of random variables
In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh–Ritz method, is introduced. Asymptotic properties of the estimator are proved, providing an upper bound for the rate of convergence under suitable mild conditions....
Optimal quantization for the one–dimensional uniform distribution with Rényi--entropy constraints
We establish the optimal quantization problem for probabilities under constrained Rényi--entropy of the quantizers. We determine the optimal quantizers and the optimal quantization error of one-dimensional uniform distributions including the known special cases (restricted codebook size) and (restricted Shannon entropy).