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

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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.

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Notes

  1. This suggestion does not affect information value of the chart since \(T_k\) set is defined by formula  (4) and with accuracy to the coordinates of the \((t_k,\tau _k)\) point is the same for all the policies sold.

  2. Further we will consider quasi-empirical distribution (20).

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Authors and Affiliations

  1. International Actuarial Advisory Company (IAAC), Llc Member of European Actuarial & Consulting Services (EURACS), Malaya Filevskaya st. 50, ap. 80, Moscow, 121433, Russia

    Valery Baskakov & Anna Bartunova

  2. RFTA, 4A Pudovkina Str., Moscow, 119285, Russia

    Valery Baskakov

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  1. Valery Baskakov
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  2. Anna Bartunova
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Correspondence to Valery Baskakov.

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Baskakov, V., Bartunova, A. Nonparametric estimation of multivariate distribution function for truncated and censored lifetime data. Eur. Actuar. J. 9, 209–239 (2019). https://doi.org/10.1007/s13385-019-00194-1

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  • DOI: https://doi.org/10.1007/s13385-019-00194-1

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