Consider studies with recurrent events data modeled by local Poisson processes with frailty, or random eeects. In a group sequential design, the increments of the test statistics are no longer independent. We explore the innuences of the frailty, and tabulate the stopping boundaries and sample size ratios to control the overall type-I and type-II error rates. Applications in an animal trial wit...

We report a novel approach for statistical image reconstruction in X-ray CT. Statistical image reconstruction depends on maximizing a likelihood derived from a statistical model for the measurements. Traditionally, the measurements are assumed to be statistically Poisson, but more recent work has argued that CT measurements actually follow a compound Poisson distribution due to the polyenergeti...

In this article, we review the concept of a Lévy copula to describe the dependence structure of a bivariate compound Poisson process. In this first statistical approach we consider a parametric model for the Lévy copula and estimate the parameters of the full dependent model based on a maximum likelihood approach. This approach ensures that the estimated model remains in the class of multivaria...

Abstract. This paper begins by defining the basic aspects of probability, including the probability space and random variables. We explore the types and qualities of random variables, as well as di↵erent distributions and their properties, with the goal of building the Poisson Process, and finally the Compound Poisson Process. This is an important counting process that can be applied to many in...

We give conditions under which the number of events which occur in a sequence of m-dependent events is stochastically smaller than a suitably defined compound Poisson random variable. The results are applied to counts of sequence pattern appearances and to system reliability. We also provide a numerical example.

The Poisson process is a stochastic counting process that arises naturally in a large variety of daily-life situations. We present a few definitions of the Poisson process and discuss several properties as well as relations to some well-known probability distributions. We further briefly discuss the compound Poisson process.

The Tweedie compound Poisson distribution is a mixture of a degenerate distribution at the origin and a continuous distribution on the positive real line. It has been applied in a wide range of fields in which continuous data with exact zeros regularly arise. Nevertheless, statistical inference based on full likelihood and Bayesian methods is not available in most statistical software, largely ...