This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they redu...

In this paper we analyse the properties of hierarchical Archimedean copulas. This class is a generalisation of the Archimedean copulas and allows for general non-exchangeable dependency structures. We show that the structure of the copula can be uniquely recovered from all bivariate margins. We derive the distribution of the copula value, which is particularly useful for tests and constructing ...

The evaluation of future cash flows and solvency capital recently gained importance in general insurance. To assist in this process, our paper proposes a novel loss reserving model, designed for individual claims in discrete time. We model the occurrence of claims, as well as their reporting delay, the time to the first payment, and the cash flows in the development process. Our approach uses d...

Although there have been a number of available tests bivariate exchangeability, i.e. symmetry for distributions, the literature is void whether multivariate distribution with more than two dimensions exchangeable or not. In this paper, permutation exchangeability distributions are proposed, which based on non-parametric combination methodology, combining tests. Numerical experiments real as wel...

The tail behavior of sums of dependent risks was considered by Wüthrich (2003) and by Alink et al. (2004, 2005) in the case where the variables are exchangeable and connected through an Archimedean copula model. It is shown here how their result can be extended to a broader class of dependence structures using multivariate extreme-value theory. An explicit form is given for the asymptotic proba...

Multivariate statistical process control deserves particular attention in the recent scenario. Though, Hotelling control chart is quite popular and widely used technique in this field but its performance is deteriorated when the underlying distribution of the quality characteristics is not following multivariate normal distribution. Hence the need of developing a non-parametric multivariate con...

A Taylor series approximation to multivariate integrals taken with respect to a multivariate probability distribution is proposed and applied to the computation of multivariate normal probabilities and conditional expectations. The approximation does not require that the multivariate distribution have a structured covariance matrix and, in its simplest form, can be written as the product of uni...