## Negative binomial version of the Lee-Carter model for mortality forecasting.(English)Zbl 1150.91426

The authors assume that the force of mortality at age $$x$$ in calendar year $$t$$ is of the form $$\exp(\alpha_{x}+\beta_{x}\kappa_{t})$$. Interpretation of the parameters is the following: $$\exp\alpha_{x}$$ is the general shape of the mortality schedule and the actual forces of mortality change according to an overall mortality index $$\kappa_{t}$$ modulated by an age response $$\beta_{x}$$. This paper develops a negative binomial regression model for estimating the $$\alpha_{x},\beta_{x}, \kappa_{t}$$. The parameters are estimated by maximum likelihood. A numerical illustration with Swedish, French and Italian data, general population is presented. The overdispersion present in population data is detected using the test statistics proposed by A. C. Cameron and P. K. Trivedi [J. Applied Econometrics, 46, 347-364 (1986)]. The goodness of fit obtained in the negative binomial regression model for death counts is examined and a comparison with the Poisson model is performed using information criteria.

### MSC:

 91B30 Risk theory, insurance (MSC2010)
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### References:

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