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We present a joint copula-based model for insurance claims and sizes. It uses bivariate copulae to accommodate for the dependence between these quantities. We derive the general distribution of the policy loss without the restrictive assumption of independence. We illustrate that this distribution tends to be skewed and multi-modal, and that an independence assumption can lead to substantial bias in the estimation of the policy loss. Further, we extend our framework to regression models by combining marginal generalized linear models with a copula. We show that this approach leads to a flexible class of models, and that the parameters can be estimated efficiently using maximum-likelihood. We propose a test procedure for the selection of the optimal copula family. The usefulness of our approach is illustrated in a simulation study and in an analysis of car insurance policies.
Monotonicity is a key qualitative prediction of a wide array of economic models derived via robust comparative statics. It is therefore important to design effective and practical econometric methods for testing this prediction in empirical analysis.
In epidemiological or demographic studies, with variable age at onset, a typical quantity of interest is the incidence of a disease (for example the cancer incidence). In these studies, the individuals are usually highly heterogeneous in terms of dat
Dependence strucuture estimation is one of the important problems in machine learning domain and has many applications in different scientific areas. In this paper, a theoretical framework for such estimation based on copula and copula entropy -- the
Use copula to model dependency of variable extends multivariate gaussian assumption. In this paper we first empirically studied copula regression model with continous response. Both simulation study and real data study are given. Secondly we give a n
Quantile regression, that is the prediction of conditional quantiles, has steadily gained importance in statistical modeling and financial applications. The authors introduce a new semiparametric quantile regression method based on sequentially fitti