The problem of evaluating the accuracy of Poisson approximation to the distribution of a sum
of independent integer-valued random variables has attracted a lot of attention in the past …

The limit theorems of probability theory are at the core of multiple models used in the broad
field of scientific research. Their main function is to replace the initial complicated stochastic …

Low-capacity scenarios have become increasingly important in the technology of Internet of
Things (IoT) and the next generation of mobile networks. Such scenarios require efficient …

Compound Poisson approximation appears naturally in situations where one deals with a
large number of rare events. It has important applications in insurance, extreme value …

We review some probabilistic properties of the sum-of-digits function of random integers.
New asymptotic approximations to the total variation distance and its refinements are also …

The Ewens sampling formula is well-known as a distribution of a random partition of the set
of integers {1, 2,..., n}. We give the condition that the number Kn of distinct components of the …

We give explicit upper bounds for the Stirling numbers of the first kind s (n, m) which are
asymptotically sharp. The form of such bounds varies according to m lying in the central or …

This work is concerned with the estimation of the intensity parameter of a stationary
determinantal point process. We consider the standard estimator, corresponding to the …

As a probability distribution on the space of probability distributions, the Dirichlet process
was introduced by Ferguson in 1973 and made a new era for nonparametric Bayes …

The distribution of the sum of 1-dependent lattice vectors with supports on coordinate axes is
approximated by a multivariate compound Poisson distribution and by signed compound …