Nonparametric estimation of multivariate distribution function for truncated and censored lifetime data
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In this article we consider a number of models for the statistical data generation in different areas of insurance, including life, pension and non-life insurance. Insurance statistics are usually truncated and censored, and often are multidimensional. There are algorithms for estimating the distribution function for such data but they are applicable for one-dimensional case. The most effective of them are implemented, for example, in SAS system. We propose a nonparametric estimation of the distribution function for multidimensional truncated-censored data in the form of quasi-empirical distribution and a simple iterative algorithm for it is calculating. The accuracy of estimating the distribution function was verified by the Monte Carlo method. A comparative analysis of the quasi-empirical distribution with alternative estimates showed that in the one-dimensional case the proposed estimate almost coincides with the estimates calculated using the HPSEVERITY procedure, which is a part of SAS ETS. We did not make the comparative analysis in the multidimensional case due to the lack of analogues of such algorithms. But our algorithm has passed years of testing in the valuation of employees liabilities in accordance with IAS 19 (Employee benefits). As an example, the article provides an assessment of the joint function of distribution of workers age and seniority of a large Russian energy enterprise. The proposed estimates can also be used in other areas, such as medicine, biology, demography, reliability, etc.
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