Alternating Runs of Geometrically Distributed Random Variables

Ascending runs of sequences of geometrically distributed random variables: a probabilistic analysis

Combinatorics of geometrically distributed random variables: run statistics

For words of length n, generated by independent geometric random variables, we consider the mean and variance, and thereafter the distribution of the number of runs of equal letters in the words. In addition, we consider the mean length of a run as well as the length of the longest run over all words of length n.

Gaps in samples of geometric random variables

In this note we continue the study of gaps in samples of geometric random variables originated in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of geometric random variables. Discrete Math. 294 (2005) 225–239] and continued in Louchard and Prodinger [The number of gaps in sequences of geometrically distributed random variables, Preprint available at 〈http://www.ulb.ac.be...

A Combinatorial and Probabilistic Study of Initial and End Heights of Descents in Samples of Geometrically Distributed Random Variables and in Permutations

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 ...

On Some Limit Distributions for Geometric Random Sums

We define and give the various characterizations of a new subclass of geometrically infinitely divisible random variables. This subclass, called geometrically semistable, is given as the set of all these random variables which are the limits in distribution of geometric, weighted and shifted random sums. Introduced class is the extension of, considered until now, classes of geometrically stable...