We consider the problem of claims reserving and estimating run-off triangles. We generalize the gamma cell distributions model which leads to Tweedie’s compound Poisson model. Choosing a suitable parametrization, we estimate the parameters of our model within the framework of generalized linear models (see Jørgensen-de Souza [2] and Smyth-Jørgensen [8]). We show that these methods lead to reaso...

A Poisson-gamma model is introduced to account for between-subjects heterogeneity and within-subjects serial correlation occurring in longitudinal count data. The model extends the usual time-constant shared frailty approach to allow time-varying serially correlated gamma frailty whilst retaining standard marginal assumptions. A composite likelihood approach to estimation and testing for serial...

We extend a recently published multivariate Bayesian cure rate model to handle interval censoring and a varying number of measurements per individual. The model assumes an unknown number of latent causes of the event in question at each repeated measurement. This number is assumed to be distributed Poisson, with rate a function of covariates multiplied by a subject-specific frailty term. The ob...

We overview the results on topic of compound Poisson approximation to distribution a sum Sn=X1+⋯+Xn (possibly dependent) random variables. indicate number open problems and discuss directions further research.

Frailty models are used in survival analysis to model unobserved heterogeneity. To study such heterogeneity by the inclusion of a random term called the frailty is assumed to multiply hazards of all subjects in the shared frailty. We study compound negative binomial distribution as frailty distribution and two different baseline distributions namely Pareto and linear failure rate distribution i...

The Ewens–Pitman sampling model (EP-SM) is a distribution for random partitions of the set {1,…,n}, with n∈N, which indexed by real parameters α and θ such that either α∈[0,1) θ>−α, or α<0 θ=−mα some m∈N. For α=0, EP-SM reduced to Ewens (E-SM), admits well-known compound Poisson perspective in terms log-series (LS-CPSM). In this paper, we consider generalisation LS-CPSM, referred as negat...