Nonparametric estimation of multivariate distribution function for truncated and censored lifetime data

TL;DR

This paper introduces a non-parametric method for estimating the multivariate distribution function of truncated and censored lifetime data, with demonstrated high accuracy through simulation and practical testing in actuarial contexts.

Contribution

It proposes a novel quasi-empirical distribution estimator and a simple iterative algorithm for multivariate truncated-censored data, applicable across various fields.

Findings

High efficiency demonstrated through simulation studies

Effective in actuarial valuation of social liabilities

Applicable in medicine, biology, demography, and reliability theory

Abstract

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.