Related papers: On the limit behaviour of finite-support bivariate…
Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action…
The paper considers multivariate discrete random sums with equal number of summands. Such distributions describe the total claim amount received by a company in a fixed time point. In Queuing theory they characterize cumulative waiting…
We study the distribution of dynamical quantities in various one-dimensional, disordered models the critical behavior of which is described by an infinite randomness fixed point. In the {\it disordered contact process}, the quenched…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…
Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This paper gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet prior…
In a paper that appeared in 2010, C. Tone proved a multivariate central limit theorem for some strictly stationary random fields of random vectors satisfying certain mixing conditions. The "normalization" of a given "partial sum" (or "block…
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to…
In a recent author's work the cyclic behavior of maxima in a hierarchical summation scheme was discovered. In the present note we show how the same phenomenon appears in the scheme of conventional summation: the distribution of maximum of…
In this paper we obtain the limit distribution for partial sums with a random number of terms following a class of mixed Poisson distributions. The resulting weak limit is a mixing between a normal distribution and an exponential family,…
We consider products of independent large random rectangular matrices with independent entries. The limit distribution of the expected empirical distribution of singular values of such products is computed. The distribution function is…
This article brings in two new discrete distributions: multidimensional Binomial distribution and multidimensional Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson…
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…
The probability that the sum of independent, centered, identically distributed, heavy-tailed random variables achieves a very large value is asymptotically equal to the probability that there exists a single summand equalling that value. We…
We investigate fractional moments and expectations of power means of complex-valued random variables by using fractional calculus. We deal with both negative and positive orders of the fractional derivatives. The one-dimensional…
This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by…
The paper deals with studying a connection of the Littlewood--Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions. It is shown that the values at zero of the concentration…
Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…
Associated to each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided. Attention,…
In this paper, we study the evolution of iterated equilibrium distributions for the Gamma and Weibull families of distributions as the iteration step increases. We characterize their moments and the pointwise limit of the distribution…
Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an…