Poisson approximation has received extensive interest in recent probability literature. The general problem is to derive bounds on the closeness of a suitable Poisson distribution to the distribution in question (usually of discrete type). To measure the degree of proximity of Poisson approximation, the following distances are usually introduced: for any two random variables X and Y taking valu...

A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to random samples of two discrete distributions. Specifically, we estimate what we call the dissimilarity probability of a sample, i.e., the probability of a d...

This paper considers the class of discrete distributions for which the distribution function is a log-concave sequence. It is shown that such distributions arise from a wide variety of circumstances in Reliability, and that these have a decreasing reversed hazard rate. After examining the closures of the class under certain key operations, sharp upper and lower bounds on the reliability functio...

The distribution of the number of trials until the first occurrence of consecutive k successes in Bernoulli trials with success probability p is called a geometric distribution of order k. This definition is due to Philippou, Georghiou and Philippou (1983). Though the distribution seems to have been interested since De Moivre (1667-1754)’s works (Todhunter (1865), Feller (1968), Johnson, Kotz a...

The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially directed meaning that certain edges are directed and others are undirected. In the paper we define a configuration model for such networks where nodes have in-, ou...

A singular Cauchy-Nicoletti problem for a system of three ordinary differential equations is considered. An approach which combines topological method of T. Ważewski and Schauder’s principle is used. Theorem concerning the existence of a solution of this problem (a graph of which lies in a given domain) is proved. Moreover, an estimation of its coordinates is obtained.

We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals. AMS 2000 subject classifications: Primary 60K35; secondary 94A17.

The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment evolution model than by the ordinary (uniform) evolution lodel. Analogously, this paper extends the random hypergraph model to a random preferential attachment ...