In this article we consider a number of models for the statistical datageneration in different areas of insurance, including life, pension andnon-life insurance. Insurance statistics are usually truncated and censored,and often are multidimensional. There are algorithms for estimating thedistribution function for such data but they are applicable for one-dimensionalcase. The most effective of them are implemented, for example, in SAS system.We propose a nonparametric estimation of the distribution function formultidimensional truncated-censored data in the form of quasi-empiricaldistribution and a simple iterative algorithm for it is calculating. Theaccuracy of estimating the distribution function was verified by the MonteCarlo method. A comparative analysis of the quasi-empirical distribution withalternative estimates showed that in the one-dimensional case the proposedestimate almost coincides with the estimates calculated using the HPSEVERITYprocedure, which is a part of SAS ETS. We did not make the comparative analysisin the multidimensional case due to the lack of analogues of such algorithms.But our algorithm has passed years of testing in the valuation of employeesliabilities in accordance with IAS 19 (Employee benefits). As an example, thearticle provides an assessment of the joint function of distribution of workersage and seniority of a large Russian energy enterprise. The proposed estimatescan also be used in other areas, such as medicine, biology, demography,reliability, etc.
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