Unimodality of Differences.
Univariate conditioning of copulas
The univariate conditioning of copulas is studied, yielding a construction method for copulas based on an a priori given copula. Based on the gluing method, g-ordinal sum of copulas is introduced and a representation of copulas by means of g-ordinal sums is given. Though different right conditionings commute, this is not the case of right and left conditioning, with a special exception of Archimedean copulas. Several interesting examples are given. Especially, any Ali-Mikhail-Haq copula with a given...
Universal distribution for infinitely divisible distributions on Frèchet space
Upper bounds for Stein-type operators.
Used of interpolatory linear positive operators for calculus the moments of the related probability distributions.
VaR bounds for joint portfolios with dependence constraints
Based on a novel extension of classical Hoeffding-Fréchet bounds, we provide an upper VaR bound for joint risk portfolios with fixed marginal distributions and positive dependence information. The positive dependence information can be assumed to hold in the tails, in some central part, or on a general subset of the domain of the distribution function of a risk portfolio. The newly provided VaR bound can be interpreted as a comonotonic VaR computed at a distorted confidence level and its quality...
Variance of periodic measure of bounded set with random position
The principal term in the asymptotic expansion of the variance of the periodic measure of a ball in under uniform random shift is proportional to the st power of the grid scaling factor. This result remains valid for a bounded set in with sufficiently smooth isotropic covariogram under a uniform random shift and an isotropic rotation, and the asymptotic term is proportional also to the -dimensional measure of the object boundary. The related coefficients are calculated for various periodic...
Variance upper bounds and a probability inequality for discrete α-unimodality
Variance upper bounds for discrete α-unimodal distributions defined on a finite support are established. These bounds depend on the support and the unimodality index α. They increase as the unimodality index α increases. More information about the underlying distributions yields tighter upper bounds for the variance. A parameter-free Bernstein-type upper bound is derived for the probability that the sum S of n independent and identically distributed discrete α-unimodal random variables exceeds its...
Variations on undirected graphical models and their relationships
We compare alternative definitions of undirected graphical models for discrete, finite variables. Lauritzen [7] provides several definitions of such models and describes their relationships. He shows that the definitions agree only when joint distributions represented by the models are limited to strictly positive distributions. Heckerman et al. [6], in their paper on dependency networks, describe another definition of undirected graphical models for strictly positive distributions. They show that...
Vector-valued Choquet-Deny theorem, renewal equation and self-similar measures
The Choquet-Deny theorem and Deny’s theorem are extended to the vector-valued case. They are applied to give a simple nonprobabilistic proof of the vector-valued renewal theorem, which is used to study the -dimension, the -density and the Fourier transformation of vector-valued self-similar measures. The results answer some questions raised by Strichartz.
Weak and strong moments of random vectors
We discuss a conjecture about comparability of weak and strong moments of log-concave random vectors and show the conjectured inequality for unconditional vectors in normed spaces with a bounded cotype constant.
Weak Convergence and Convergence in the Mean of Distribution Functions.
Weak convergence of linear rank statistics
Weighting, likelihood ratio order and life distributions
We use weighted distributions with a weight function being a ratio of two densities to obtain some results of interest concerning life and residual life distributions. Our theorems are corollaries from results of Jain et al. (1989) and Bartoszewicz and Skolimowska (2006).
What are cumulants?
When is a Riesz distribution a complex measure?
Let be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by . I give an elementary proof of the necessary and sufficient condition for to be a locally finite complex measure (= complex Radon measure).
Wiener functionals of second order and their Lévy measures.
Wrapped Distributionsand Measurement Errors.
Zeros of smallest modulus of functions resembling exp(z).
Аналитическое уточнение теоремы Хайде о линейных формах от независимых случайных величин