LetX be a random variable (RV), distributed according to the geometric distribution with parameter p (geom(p)): P(X = k) = pq, with q = 1 − p. We consider a sequence X1X2 . . . Xn of independent RVs. We also speak about words a1 . . . an; there is some interest of combinatorial parameters of such words, generated by independent geometric random variables. In this paper we continue the study of ...

A random variableX is geometrically infinitely divisible iff for every p ∈ (0, 1) there exists random variable Xp such that X d = ∑T (p) k=1 Xp,k, where Xp,k’s are i.i.d. copies of Xp, and random variable T (p) independent of {Xp,1, Xp,2, . . .} has geometric distribution with the parameter p. In the paper we give some new characterization of geometrically infinitely divisible distribution. The...

A random-walk Metropolis sampler is geometrically ergodic if its equilibrium density is super-exponentially light and satisfies a curvature condition (Jarner and Hansen, 2000). Many applications, including Bayesian analysis with conjugate priors of logistic and Poisson regression and of log-linear models for categorical data result in posterior distributions that are not super-exponentially lig...

This paper presents some refinements of a rare event simulation algorithm developped in [1] for estimating the probability of connection of two nodes s and t in an undirected graph G representing a communication network where nodes are perfect but links can fail. The method proposed in [1] makes use of disjoint paths (that is, with no common link) and samples a geometric variable representing t...

Let G be a graph in which each vertex initially has weight 1. In each step, the weight from a vertex u to a neighbouring vertex v can be moved, provided that the weight on v is at least as large as the weight on u. The total acquisition number of G, denoted by at(G), is the minimum cardinality of the set of vertices with positive weight at the end of the process. In this paper, we investigate r...