Exploring the Health Status of a Population: A Simple Health State Model vs the Gompertz Model

  • Christos H. Skiadas
Part of the The Springer Series on Demographic Methods and Population Analysis book series (PSDE, volume 46)


We present a method to formulate the Health State or Health Status curve of a population from the Gompertz model thus providing a useful tool to demographers, actuaries, policy makers, health people and organizations and sociologists. The model is presented along with a simple first exit time model and another “Best Fit” model. A method of finding the corrected health state or health status is also presented.


  1. Gompertz, B. (1825). On the nature of the function expressing of the law of human mortality. Philosophical Transactions of the Royal Society, 36, 513–585.CrossRefGoogle Scholar
  2. Janssen, J., & Skiadas, C. H. (1995). Dynamic modelling of life-table data. Applied Stochastic Models and Data Analysis, 11(1), 35–49.CrossRefGoogle Scholar
  3. Jennen, C. (1985). Second-order approximation for Brownian first exit distributions. Annals of Probability, 13, 126–144.CrossRefGoogle Scholar
  4. Jennen, C., & Lerche, H. R. (1981). First exit densities of Brownian motion through one-sided moving boundaries. Zeitschrift Wahrscheinlichkeitstheorie und verwandte Gebiete, 55, 133–148.CrossRefGoogle Scholar
  5. Lerche, H. R. (1986). Boundary crossing of Brownian motion. Berlin: Springer.CrossRefGoogle Scholar
  6. Sanders, B. S. (1964). Measuring community health levels. American Journal of Public Health, 54, 1063–1070.CrossRefGoogle Scholar
  7. Skiadas, C. H. (2011, October 1). A life expectancy study based on the deterioration function and an application to Halley’s Breslau data. arXiv:1110.0130v1 [q-bio.PE].Google Scholar
  8. Skiadas, C. H., & Skiadas, C. (2010a). Comparing the Gompertz type models with a first passage time density model. In C. H. Skiadas (Ed.), Advances in data analysis (pp. 203–209). Boston: Springer/Birkhauser.CrossRefGoogle Scholar
  9. Skiadas, C. H., & Skiadas, C. (2010b). Development, simulation and application of first exit time densities to life table data. Communications in Statistics, 39, 444–451.CrossRefGoogle Scholar
  10. Skiadas, C. H., & Skiadas, C. (2013a). The health state function of a population. Athens: ISAST.Google Scholar
  11. Skiadas, C. H., & Skiadas, C. (2013b). Supplement: The health state function of a population. Athens: ISAST.Google Scholar
  12. Skiadas, C. H., & Skiadas, C. (2014). The first exit time theory applied to life table data: The health state function of a population and other characteristics. Communications in Statistics-Theory and Methods, 43(7), 1585–1600.CrossRefGoogle Scholar
  13. Skiadas, C. H., & Skiadas, C. (2015). Exploring the state of a stochastic system via stochastic simulations: An interesting inversion problem and the health state function. Methodology and Computing in Applied Probability, 17(4), 973–982.CrossRefGoogle Scholar
  14. Skiadas, C. H., & Skiadas, C. (2017). Exploring the health state of a population by dynamic modeling methods. Springer.
  15. Sullivan, D. F. (1966). Conceptual problems in developing an index of health (U.S. Department of HEW, Public Health Service Publication No. 1000, Series 2, No. 17). Washington, DC: U.S. Department of Health, Education and Welfare.Google Scholar
  16. Sullivan, D. F. (1971). (National Center for Health Statistics): A single index of mortality and morbidity. HSMHA Health Reports, 86, 347–354.CrossRefGoogle Scholar
  17. Torrance, G. W. (1976). Health status index models: A unified mathematical view. Management Science, 22(9), 990–1001.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ManLabTechnical University of CreteChaniaGreece

Personalised recommendations