A New Class of Counting Distributions Embedded in the Lee–Carter Model for Mortality Projections: A Bayesian Approach

Yaser Awad, Shaul K. Bar-Lev and Udi Makov
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Yaser Awad: Sakhnin Academic College, Galilee St. 100, Sakhnin 30810, Israel
Shaul K. Bar-Lev: Faculty of Industrial Engineering and Technology Management, HIT—Holon Institute of Technology, 52 Golomb Street, Holon 5810201, Israel
Udi Makov: Actuarial Research Center, University of Haifa, 199 Aba Khoushy Ave. Mount Carmel, Haifa 3498838, Israel

Risks, 2022, vol. 10, issue 6, 1-17

Abstract: The Lee–Carter model, the dominant mortality projection modeling in the literature, was criticized for its homoscedastic error assumption. This was corrected in extensions to the model based on the assumption that the number of deaths follows Poisson or negative binomial distributions. We propose a new class of families of counting distributions, namely, the ABM class, which belongs to a wider class of natural exponential families. This class is characterized by its variance functions and contains the Poisson and the negative binomial distributions as special cases, offering an infinite class of additional counting distributions to be considered. We are guided by the principle that the choice of distribution should be made from a pool of distributions as large as possible. To this end, and following a data mining approach, a training set of historical mortality data of the population could be modeled using the ABM’s rich choice of distributions, and the chosen distribution should be the one that proved to offer superior projection results on a test set of mortality data. As an alternative to parameter estimation via the singular value decomposition used in the classical Lee–Carter model, we adopted Bayesian estimation, harnessing the Markov Chain Monte Carlo methodology. A numerical study demonstrates that when fitting mortality data using this new class of distributions, while traditional distributions may provide desirable projections for some populations, for others, alternative distributions within the ABM class can potentially produce superior results for the entire population or particular age groups, such as the oldest-old.

Keywords: Lee–Carter; counting distributions; mortality projections; natural exponential family (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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