In the present paper we consider compound Poisson approximation by Stein’s method for dissociated random variables. We present some applications to problems in system reliability. In particular, our examples have the structure of an incomplete U-statistics. We mainly apply techniques from Barbour and Utev, who gave new bounds for the solutions of the Stein equation in compound Poisson approxima...

A mixed Poisson approximation and a Poisson approximation for the length of the longest exact match of a Markov sequence across another sequence are provided, where the match is required to start at position 1 in the first sequence. This problem arises when looking for suitable anchors in whole genome alignments. ∗AMS 2000 subject classifications. 62E17, 92D20. †

The configurational entropy of nanoscale solutions is discussed in this paper. As follows from the comparison of the exact equation of Boltzmann and its Stirling approximation (widely used for both macroscale and nanoscale solutions today), the latter significantly over-estimates the former for nano-phases and surface regions. On the other hand, the exact Boltzmann equation cannot be used for p...

In the classical occupancy scheme with infinitely many boxes, n balls are thrown independently into boxes 1, 2, . . ., with probabilities pj , j ≥ 1. We establish approximations to the distributions of the summary statistics Kn, the number of occupied boxes, and Kn,r, the number of boxes containing exactly r balls, within the family of translated Poisson distributions. These are shown to be of ...

We consider a general class of high order weak approximation schemes for stochastic differential equations driven by Lévy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the Lévy process with a high order scheme for the Brownian driven component, applied between the jump times. The overall approximation is analyzed using a stochastic...

We implement the recently introduced Poisson approximation on a density dependent jump process corresponding to a simple, but not exactly solvable, epidemiological model. Statistics produced with 10 independent realizations of the Feller process are compared with equivalent statistics produced with Poisson, proper Gaussian and diffusion realizations. While in the Poisson approximation the stati...

in order to study the relationship between random boolean sets and some explanatory variables, this paper introduces a propagation model. this model can be applied when corresponding poisson process of the boolean model is related to explanatory variables and the random grains are not affected by these variables. an approximation for the likelihood is used to find pseudo-maximum likelihood esti...

Motivated, in part, by the desire to develop an information-theoretic foundation for compound Poisson approximation limit theorems (analogous to the corresponding developments for the central limit theorem and for simple Poisson approximation), this work examines sufficient conditions under which the compound Poisson distribution has maximal entropy within a natural class of probability measure...