A comparison of parametric models for mortality graduation. Application to mortality data of the Valencia Region

  1. Sala Garrido, Ramón
  2. Montes Suay, Francisco
  3. Debón Aucejo, Ana María
Revista:
Sort: Statistics and Operations Research Transactions

ISSN: 1696-2281

Any de publicació: 2005

Volum: 29

Número: 2

Pàgines: 269-287

Tipus: Article

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Altres publicacions en: Sort: Statistics and Operations Research Transactions

Resum

HolaThe parametric graduation of mortality data has as its objective the satisfactory estimation of the death rates based on mortality data but using an age-dependent function whose parameters are adjusted from the crude rates obtainable directly from the data. This paper proposes a revision of the most commonly used parametric methods and compares the results obtained with each of them when they are applied to the mortality data for the Valencia Region. As a result of the comparison, we conclude that the Gompertz-Makeham functions estimated by means of generalized linear models lead to the best results. Our working method is of additional interest for being applicable to mortality data for a wide range of ages from any geographical conditions, allowing us to select the most appropriate life table for the case in hand. MSC: 62P05 Keywords: Gompertz-Makeham functions, Heligman and Pollard¿s laws, parametric graduation HolaLa gradualitzaci¿o param`etrica de dades de mortalitat t¿e com a objectiu l¿estimaci¿o correcta de taxes de mort a partir de les dades de mortalitat mitjanc¿ant una funci¿o que dep`en de l¿edat, els par`ametres de la qual s¿ajusten a partir de les taxes ¿brutes¿ de mortalitat obtingudes directament de les dades. Aquest article presenta una revisi¿o dels models param`etrics m¿es habituals i la seua aplicaci¿o a les dades de mortalitat del Pa¿ýs Valenci`a. Com a conseq¿u`encia de la comparaci¿o dels resultats obtinguts amb els diferents models, es conclou que les funcions de Gompertz-Makeham estimades mitjanc¿ant models lineals generalitzats condueixen als millors resultats. El m`etode de treball que es presenta t¿e inter`es suplementari per ser aplicable a dades de mortalitat per a un ampli rang d¿edats i per a qualsevol `ambit geogr`afic, permetent en cada cas seleccionar la millor taula de vida. Paraules clau: funcions de Gompertz-Makeham, lleis de Heligman i Pollard¿s, gradualitzaci ¿o param`etrica

Referències bibliogràfiques

  • Benjamin, B. and Pollard, J. (1992). The Analysis of Mortality and Other Actuarial Statistics, 6th edition. London: Butterworth-Heinemann.
  • Butt, Z. and Haberman, S. (2004). Application of frailty-based mortality models using generalized linear models. Astin Bulletin, 34, 175-197.
  • Congdon, P. (1993). Statistical graduation in local demographic analysis and projection. Journal of the Royal Statistical Society A, 156, 237-270.
  • Debon, A., Montes, F., and Sala, R. (2003). Graduaci ´ on de datos de mortalidad. In ´ Actas del 27 Congreso Nacional de Estad´ıstica e Investigaci´on Operativa, Lleida, Espana. Universitat de Lleida, 562-578. ˜
  • Dellaportas, P., Smith, A., and Stavropoulos, P. (2001). Bayesian analysis of mortality data. Journal of the Royal Statistical Society A, 164, 275-291.
  • Felipe, M. and Guillen, M. (1999). ´ Evoluci´on y Predicci´on de las Tablas de Mortalidad Din´amicas para la Poblaci´on Espa˜nola. Cuadernos de la Fundacion, Fundaci ´ on Mapfre Estudios. ´
  • Forfar, D., McCutcheon, J., and Wilkie, A. (1988). On graduation by mathematical formula. Journal of the Institute of Actuaries, 115, 1-149.
  • Gavin, J., Haberman, S., and Verrall, R. (1993). Moving weighted average graduation using kernel estimation. Insurance: Mathematics and Economics, 12, 113-126.
  • Gavin, J., Haberman, S., and Verrall, R. (1995). Graduation by kernel and adaptive kernel methods with a boundary correction. Transactions. Society of Actuaries, XLVII, 173-209.
  • Gerber, H. (1997). Life Insurance Mathematics. Berlin: Springer-Verlag.
  • Gompertz, B. (1825). On the nature of the function of the law of human mortality and on a new mode of determining the value of life contingencies. Philosophical Transactions of The Royal Society, 115, 513-585.
  • Haberman, S. and Renshaw, A. (1996). Generalized linear models and actuarial science. The Statistician, 45, 407-436.
  • Heligman, L. and Pollard, J. (1980). The age pattern of mortality. Journal of the Institute of Actuaries, 107, 49-80.
  • INE (1997). Evoluci´on de la poblaci´on de Espa˜na entre los censos de 1981 y 1991. Madrid: Instituto Nacional de Estad´ıstica.
  • INE (2001). Evoluci´on de la poblaci´on de Espa˜na entre los censos de 1991 y 2001. Madrid: Instituto Nacional de Estad´ıstica.
  • Lambert, J. (1772). Anmerkungen uber die Sterblichkeit, Todtenlisten, Gerburthen und Ehen. ¨ in Beytr¨age, 3, 475-599.
  • London, D. (1985). Graduation: the Revision of Estimates. Actex Publication, Winsted, Cunnecticud.
  • Makeham, W. (1860). On the law of mortality. Journal of the Institute of Actuaries, 13, 325-358.
  • Navarro, E. (1991). Tablas de Mortalidad de la Poblaci´on Espa˜nola 1982. Metodolog´ıa y Fuentes. Madrid: Mapfre.
  • Navarro, E., Ferrer, R., Gonzalez, C., and Nave, J. (1995). Tablas de Mortalidad de la Comunidad Valenciana 1990-91. Censos de Poblaci´o i Habitatges, volume I. IVE, Valencia.
  • Renshaw, A. (1991). Actuarial graduation practice and generalised linear models. Journal of the Institute of Actuaries, 118, 295-312.
  • Renshaw, A., Haberman, S., and Hatzopoulos, P. (1997). On the duality of assumptions underpinning the construction of life tables. Astin Bulletin, 27, 5-22.
  • Renshaw, A. and Hatzopoulos, P. (1996). On the graduation of amounts. British Actuarial Journal, 2, 185- 205.
  • Thiele, P. (1972). On a mathematical formula to express the rate of mortality throughout the whole of life. Journal of the Institute of Actuaries, 16, 313-329.
  • Verrall, R. (1996). A unified framework for graduation. Actuarial Research Paper, 91, 2-25.
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