Dufresne et al. (1991) introduced a general risk model defined as the limit of compound Poisson processes. Such model is either a compound Poisson process itself or a strictly increasing Lévy process. Their construction is based on a nonnegative non-increasing function Q that governs the jumps of the process. This function, it turns out, is the tail of the Lévy measure of the process. We discus...

The theory of exponential dispersion models was applied to construct a stochastic model for heterogeneities in regional organ blood flow as inferred from the deposition of labeled microspheres. The requirements that the dispersion model be additive (or reproductive), scale invariant, and represent a compound Poisson distribution, implied that the relative dispersion (RD = standard deviation/mea...

Classical peaks over threshold analysis is widely used for statistical modeling of sample extremes, and can be supplemented by a model for the sizes of clusters of exceedances. Under mild conditions a compound Poisson process model allows the estimation of the marginal distribution of threshold exceedances and of the mean cluster size, but requires the choice of a threshold and of a run paramet...

BACKGROUND There is little certainty as to the prevalence of frailty in Canadians in younger adulthood. This study examines and compares the prevalence of frailty in Canadians 18-79 years old using the Accumulation of Deficits and Fried models of frailty. METHODS The Canadian Health Measures Study data were used to estimate the prevalence of frailty in adults 18-79 years old. A 23-item Frailt...

Survival analyses are greatly used in medical research especially frailty models which are mostly used to account for heterogeneity in time-to-event. Over the years treatment of cancer has progressed with some patients being cured from different type of cancer. Survival analysis is more focused on subjects that are less at risk of recurrences, metastasis or death after the first treatment as th...

Biological dosimetry based on chromosome aberration scoring in peripheral blood lymphocytes enables timely assessment of the ionizing radiation dose absorbed by an individual. Here, new Bayesian-type count data inverse regression methods are introduced for situations where responses are Poisson or two-parameter compound Poisson distributed. Our Poisson models are calculated in a closed form, by...

b a c k g r o u n d & aim: multi-state models can help better understand the process of chronic diseases such as cancers.  these models  are influenced  by assumptions  like individual  homogeneity.  this study aimed to investigate the effect of lack of individual homogeneity  assumption  in multi-state models. methods & materials: to investigate the effect of lack of individual homogeneity ass...

Sufficient conditions are developed, under which the compound Poisson distribution has maximal entropy within a natural class of probability measures on the nonnegative integers. Recently, one of the authors [O. Johnson, Stoch. Proc. Appl., 2007] used a semigroup approach to show that the Poisson has maximal entropy among all ultra-log-concave distributions with fixed mean. We show via a non-tr...

Abstract: We give a simple development of the concentration properties of compound Poisson measures on the nonnegative integers. A new modification of the Herbst argument is applied to an appropriate modified logarithmic-Sobolev inequality to derive new concentration bounds. When the measure of interest does not have finite exponential moments, these bounds exhibit optimal polynomial decay. Sim...

Compound Poisson approximation is a useful tool in a variety of applications, including insurance mathematics, reliability theory, and molecular sequence analysis. In this paper, we review the ways in which Stein's method can currently be used to derive bounds on the error in such approximations. The theoretical basis for the construction of error bounds is systematically discussed, and a numbe...