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 usedin other areas, such as medicine, biology, demography,  reliability, etc.
A number of models for generating statistical data in various fields of insurance, including life insurance, pensions, and general insurance have been considered. It is shown that the insurance statistics data, as a rule, are truncated and censored, and often multivariate. We propose a non-parametric estimation of the distribution function for multivariate truncated-censored data in the form of a quasi-empirical distribution and a simple iterative algorithm for its construction. To check the accuracy of the proposed evaluation of the distribution function for truncated-censored data, simulation studies have been conducted, which showed its high efficiency. The proposed estimates have been tested for many years by the IAAC Group of Companies in the actuarial valuation of corporate social liabilities according to IAS 19 Employee Benefits. Apart from insurance, some results of the work can be used, for example in medicine, biology, demography, mathematical theory of reliability, etc.
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In this article we consider a
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the statistical data generation in different areas
generating statistical data in various fields
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, pension and non-life insurance . Insurance statistics are usually
insurance, pensions, and general insurance have been considered. It is shown that the insurance statistics data, as a rule, are
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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.
multivariate.
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nonparametric
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multidimensional
multivariate
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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
its construction. To check the accuracy of the proposed evaluation of the distribution function for truncated-censored data, simulation studies have been conducted, which showed its high efficiency. The proposed estimates have been tested for many years by the IAAC Group of Companies in the actuarial valuation of corporate social liabilities according to
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(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 usedin other areas, such as
Employee Benefits. Apart from insurance, some results of the work can be used, for example in
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mathematical theory of