Limit theorems for mixed max-sum processes with renewal stopping

This article is devoted to the investigation of limit theorems for mixed max-sum processes with renewal type stopping indexes. Limit theorems of weak convergence type are obtained as well as functional limit theorems.Comment: Published at http://dx.doi.org/10.1214/105051604000000215 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Some representations of the multivariate Bernoulli and binomial distributions

Multivariate but vectorized versions for Bernoulli and binomial distributions are established using the concept of Kronecker product from matrix calculus. The multivariate Bernoulli distribution entails a parameterized model, that provides an alternative to the traditional log-linear model for binary variables.multivariate Bernoulli distribution multivariate binomial distribution log-linear models categorical data

The structure distribution in a mixed Poisson process

We use a variety of real inversion formulas to derive the structure distribution in a mixed Poisson process. These approaches should prove to be useful in applications, e.g., in insurance where such processes are very popular