Before revision:  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).
After revision:  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 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).