- Author
- Szymański Andrzej (University of Lodz, Poland), Rossa Agnieszka (University of Lodz, Poland)
- Title
- The Complex-Number Mortality Model (CNMM) Based on Orthonormal Expansion of Membership Functions
- Source
- Statistics in Transition, 2021, vol. 22, nr 3, s. 31-57, tab., wykr., bibliogr. 28 poz.
- Keyword
- Umieralność, Matematyczne modele umieralności, Funkcje
Mortality, Mathematical model of mortality, Functions - Note
- summ.
- Abstract
- The paper deals with a new fuzzy version of the Lee-Carter (LC) mortality model, in which mortality rates as well as parameters of the LC model are treated as triangular fuzzy numbers. As a starting point, the fuzzy Koissi-Shapiro (KS) approach is recalled. Based on this approach, a new fuzzy mortality model - CNMM - is formulated using orthonormal expansions of the inverse exponential membership functions of the model components. The paper includes numerical findings based on a case study with the use of the new mortality model compared to the results obtained with the standard LC model.(original abstract)
- Accessibility
- The Main Library of the Cracow University of Economics
The Library of Warsaw School of Economics
The Library of University of Economics in Katowice - Full text
- Show
- Bibliography
- Bongaarts, J., (2005). Long-range trends in adult mortality: Models and projection methods, Demography, 42(1), pp. 23-49.
- Booth, H., Hyndman, R. J., Tickle, L., De Jong, P., (2006). Lee-Carter mortality forecasting: A multi-country comparison of variants and extensions models, Demographic Research, 15(9), pp. 289-310.
- Booth, H., Maindonald, J., Smith, L., (2002). Applying Lee-Carter under conditions of variable mortality decline. Population Studies, 56 (3), 325-333.
- Bozik, J. E., Bell, W. R., (1987). Forecasting Age Specific Fertility Using Principal Components, Bureau of the Census Statistical Research Division Washington D.C., CENSUS/SRD/RR-87/19, https://www.census.gov/srd/papers/pdf/rr87-19.pdf.
- Brouhns, N., Denuit, M., Vermunt, J. K., (2002). A Poisson log-bilinear regression approach to the construction of projected lifetables, Insurance: Mathematics and Economics, 31(3), pp. 373-393.
- Cairns, A. J. G., Blake, D., Dowd, K., (2006). A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration, Journal of Risk and Insurance, 73(4), pp. 687-718.
- Currie, I. D., Durban, M., Eilers, P. H. C., (2004). Smoothing and forecasting mortality rates, Statistical Modelling, 4(4).
- Danesi, I. L., Haberman, S., Millossovich, P., (2015). Forecasting mortality in subpopulations using Lee-Carter type models: A comparison, Insurance: Mathematics and Economics, 62(4), pp. 151-161.
- De Jong, P., Tickle, L., (2006). Extending Lee-Carter mortality forecasting. Mathematical Population Studies, 13(1), pp. 1-18.
- Diamond, P., (1988), Fuzzy least-squares, Information Sciences, 46(3), pp. 141-157.
- Haberman, S., Renshaw, A., (2012). Parametric mortality improvement rate modelling and projecting, Insurance: Mathematics and Economics, 50(3), pp. 309-333.
- Heligman, L., Pollard, J. H., (1980). The age pattern of mortality, Journal of the Institute of Actuaries, 170, pp. 49-80.
- Horiuchi, S., Coale, A. J., (1990). Age patterns of mortality for older women: An analysis using the age-specific rate of mortality change with age, Mathematical Population Studies, 2(4), 245-267.
- Human Fertility Database. Max Planck Institute for Demographic Research (Germany) and Vienna Institute of Demography (Austria). Available at www.humanfertility.org.
- Ishikawa, S., (1997). Fuzzy inferences by algebraic method, Fuzzy Sets and Systems, 87, pp. 181-200.
- Koissi, M.-C., Shapiro, A. F., (2006). Fuzzy formulation of the Lee-Carter model for mortality forecasting, Insurance: Mathematics and Economics, 39, pp. 287-309.
- Kosiński, W., Prokopowicz, P., Ślęzak, D., (2003). Ordered Fuzzy Numbers, Bull. Polish Acad. Sci. Math., 51, pp. 327-338.
- Lee, R. D., Carter, L., (1992). Modeling and forecasting the time series of U.S. mortality, Journal of the American Statistical Association, 87, pp. 659-671.
- Milevsky, M. A., Promislow, S. D., (2001). Mortality Derivatives and the Option to Annuitise,Insurance: Mathematics and Economics, 29, pp. 299-318.
- Pitacco, E., Denuit, M., Haberman, S., Olivieri, A., (2009). Modelling Longevity Dynamics for Pensions and Annnuity Business, Oxford University Press.
- Prokopowicz, P., Czerniak, J., Mikołajewski, D., Apiecionek, Ł., Ślęzak, D. (eds.), (2017). Ordered Fuzzy Numbers: Definitions and Operations, Studies in Fuzziness and Soft Computing, vol. 356, Springer Open.
- Renshaw, A. E., Haberman, S., (2003). Lee-Carter mortality forecasting with age specific enhancement, Insurance: Mathematics and Economics, 33(2), pp. 255-272.
- Renshaw, A., Haberman, S., Hatzopoulos, P., (1996). The modelling of recent mortality trends in United Kingdom male assured lives. British Actuarial Journal, 2, pp. 449-477.
- Rossa, A., Socha, L., Szymański, A., (2011). Analiza i modelowanie umieralności w ujęciu dynamicznym (in Polish), University of Lodz Press, Łódź.
- Rossa, A., Socha, L., Szymański, A., (2017). Hybrid Dynamic and Fuzzy Models of Mortality. University of Lodz Press.
- Szymański, A., Rossa, A., (2014). Fuzzy mortality model based on Banach algebra, International Journal of Intelligent Technologies and Applied Statistics, 7,pp. 241-265.
- Szymański, A., Rossa, A., (2017). Improvement of fuzzy mortality model by means of algebraic methods, Statistics in Transition, 18, pp. 701-724.
- Tuljapurkar, S., Li, N., Boe, C., (2000). A universal pattern of mortality decline in the G7 countries, Nature, 405, pp. 789-792.
- Cited by
- ISSN
- 1234-7655
- Language
- eng
- URI / DOI
- http://dx.doi.org/10.21307/stattrans-2021-026