Properties of future lifetime distributions and estimation

Abstract

Distributional properties of continuous future lifetime of an individual aged x have been studied. The expressions for moments, coecients of skewness and kurtosis have been derived when newborn's lifetime follows dierent distributions. The maximum likelihood (ML) estimation of the parameters of future lifetime's distributions has been explored for whole life and term assurance contracts. Simulations have been carried out to find the ML estimates and the corresponding root mean square errors.

Keywords

• Future Lifetime,Whole life assurance,Term assurance,Maximum Likelihood Estimation,Censoring

References

1. Borowiak, D. S. and Shapiro, A. F. Financial and Actuarial Statistics: An Introduction. A Series of Textbooks and Monographs, Marcel Dekker Publication, New York, 2003.
2. Bowers, N. L., Gerber, H. U., Hickman, J. C, Jones, D. A. and Nesbitt, C. J. Actuarial Mathematics, The Society of Actuaries, USA, 1997.
3. Dickson, D. C. M., Hardy, M. R. and Waters, H. R. Actuarial Mathematics for Life Con- tingent Risks, International Series on Actuarial Science, Cambridge University Press, UK, 2009.
4. Gerber, H.U. Life Insurance Mathematics, Springer, Germany, 1990.
5. International Actuarial Notation. Journal of the Institute of Actuaries, 75, 121-129, 1949.
6. Jain, K. and Kapoor, H. P. S. Ageing Properties of Curtate Future Life Time. Sri Lankan Journal of Applied Statistics, 14 (1), 55-84, 2013.
7. Johnson, N. L., Balakrishnan, N. and Kotz, S. Continuous Univariate Distributions 1, Wiley Series in Probability and Statistics, John Wiley and Sons, USA, 1994.
8. Johnson, N. L., Balakrishnan, N. and Kotz, S. Continuous Univariate Distributions 2, Wiley Series in Probability and Statistics, John Wiley and Sons, USA, 1995.

9. Kleiber, C. and Kotz, S. Statistical Size Distributions in Economics and Actuarial Sciences, John Wiley and Sons, New Jersey, Hoboken, 2003.
10. Klein, J. P. and Moeschberger, M. L. Survival Analysis: Techniques for Censored and Truncated Data, Second edition, Springer Verlag, USA, 2003.
11. Lai, C. D. and Xie, M. Stochastic Ageing and Dependence for Reliability, Springer, USA, 2006.
12. Zhu, Y. J. Actuarial Model: Life Insurance and Annuity, Series in Actuarial Science, Inter- national Press, USA, 2007.