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Life Expectancy Estimates

The best fit model is a combination of a model derived from the first exit time theory of a stochastic process with a Gompertzian correction for the ages from 15 to 30 years. 
For the best fit model go to the Health State Model webpage

Life_Expectancy_at_Birth_USA_Females_Forecasts.jpg
Life Expectancy at Birth in USA, Females (Fit and Forecasts)

This picture illustrates the estimation and forecasts of the Life Expectancy at Birth (USA Females) based on the theory presented in the following paper titled: "A Life Expectancy Study based on the Deterioration Function and an Application to Halley’s Breslau Data". In this case we move the estimated values for the Deterioration Function and from the DTR System to the right thus achieving better forecasts. The estimates are included in the following Table.

Related Paper

Table_Life_Expectancy_Estimates_USA_Females.gif

Life_Expectancy_at_Birth_Japan_Females_Forecasts.jpg
Life Expectancy at Birth in Japan, Females (Fit and Forecasts)

 

This picture illustrates the estimated values and forecasts of the Life Expectancy at Birth (Japan Females) based on the theory presented below.

The estimates are included in the following Table. 

 

Table_Life_Expectancy_Estimates_Japan_Females.gif

Life_Expectancy_at_Birth_UK_Females_Forecasts.jpg
Life Expectancy at Birth in UK, Females (Fit and Forecasts)

 

This picture illustrates the estimated values and forecasts of the Life Expectancy at Birth in UK (Females) based on the theory presented below.

The estimates are included in the following Table. 
 

Table_Life_Expectancy_at_Birth_UK_Females_Forecasts.gif

Life_Expectancy_at_Birth_Portugal_Females_Forecasts.jpg

 

 

This picture illustrates the estimated values and forecasts of the Life Expectancy at Birth in Portugal (Females) based on the theory presented below.

The estimates are included in the following Table.

Table_Life_Expectancy_at_Birth_Portugal_Females_Forecasts.gif

  
 

A Life Expectancy Study based on the Deterioration Function and an Application to Halley’s Breslau Data*

*Paper Version: October 1, 2011, http://arxiv.org/abs/1110.0130

*Paper version, October 13, 2011

Here download the latest version of the Regression model in Excel

Christos H Skiadas

Technical University of Crete, Data analysis and forecasting laboratory, Chania, Crete, Greece

E-mail: skiadas@cmsim.net

 Abstract: Further to the proposal and application of a stochastic methodology and the resulting first exit time distribution function to life table data we introduce a theoretical framework for the estimation of the maximum deterioration age and to explore on how “vitality,” according to Halley and Strehler and Mildvan, changes during the human lifetime. The mortality deceleration or mortality leveling-off is also explored. The effect of the deterioration over time is estimated as the expectation that an individual will survive from the deterioration caused in his organism by the deterioration mechanism. A method is proposed and the appropriate software was developed for the estimation of life expectancy. Several applications follow.

The method was applied to the Halley life table data of Breslau. Extrapolations are done showing a gradual improvement of vitality mechanisms during last centuries.

Keywords: Life expectancy, Life expectancy at birth, Deterioration function, Late-Life Mortality Deceleration, Mortality Leveling-off, Mortality Plateaus Vitality, Halley Breslau data.

Click here to download the paper: A Life Expectancy Study based on the Deterioration Function and an Application to Halley Breslau Data (13-10-2011 version)

Conclusions

 We have developed and applied a new theoretical framework for analyzing mortality data. The work starting several years ago was based on the stochastic theory and the derivation of a first exit time distribution function suitable for expressing the human mortality. Furthermore we have explored on how we could model the so-called “vitality” of a person or the opposite term the deterioration of an organism and to provide a function, the deterioration function, which could be useful for sociologists, police makers and the insurance people in making their estimates and plan the future.

 Acknowledgments

 The data used can be downloaded from the Human Mortality Database at: http://www.mortality.org or from the statistical year-books of the countries studied.

The Program

A computer program (IM-model-DTR-Life_Tables) was developed to be able to make the necessary computations related to this study. Furthermore the program estimates the life expectancy tables by based on the mortality and population data. The life expectancy is also estimated by based on the fitting curve thus making more accurate the related estimations. The program and the related theory can be found in the website: http://www.cmsim.net. The program is developed in Excel 2003 and it is very easy to use without any special tool.

Here download the latest version of the Regression model in Excel

References

 A. Economos, A non-Gompertzian paradigm for mortality kinetics of metazoan animals and failure kinetics of manufactured products. Age, vol.2, 74-76 (1979).

A. Economos, Kinetics of metazoan mortality. J. Social Biol. Struct., 3, 317-329 (1980).

B. Gompertz, On the nature of the function expressive of the law of human
mortality, and on the mode of determining the value of life contingencies, Philosophical Transactions of the Royal Society of London A 115, 513-585 (1825).

J. Graunt, Natural and Political Observations Made upon the Bills of Mortality, First Edition, 1662; Fifth Edition (1676).

M. Greenwood and J. O. Irwin, The biostatistics of senility, Human Biology, vol.11, 1-23 (1939).

S. Haberman and T. A. Sibbett, History of Actuarial Science, London, UK: William Pickering, (1995).

E. Halley, An Estimate of the Degrees of Mortality of Mankind, Drawn from the Curious Tables of the Births and Funerals at the City of Breslau, with an Attempt to Ascertain the Price of Annuities upon Lives, Philosophical Transactions, Volume 17, pp. 596-610 (1693).

L. M. A. Heligman and J. H. Pollard, The Age Pattern of mortality, Journal of the Institute of Actuaries 107, part 1, 49-82 (1980).

J. Janssen and C. H. Skiadas, Dynamic modelling of life-table data, Applied Stochastic Models and Data Analysis, 11, 1, 35-49 (1995).

N. Keyfitz and H. Caswell, Applied Mathematical Demography, 3rd ed., Springer (2005).

R. D. Lee and L. R. Carter, Modelling and forecasting U.S. mortality. J. Amer. Statist. Assoc. 87 (14), 659–675 (1992).

W. M. Makeham, On the Law of Mortality and the Construction of Annuity Tables, J. Inst. Act. and Assur. Mag. 8, 301-310, (1860).

C. H. Skiadas and C. Skiadas, A modeling approach to life table data, in Recent Advances in Stochastic Modeling and Data Analysis, C. H. Skiadas, Ed. (World Scientific,  Singapore), 350–359 (2007).

C. H. Skiadas, C. Skiadas, Comparing the Gompertz Type Models with a First Passage Time Density Model, in Advances in Data Analysis, C. H. Skiadas Ed. (Springer/Birkhauser, Boston), 203-209 (2010).

C. Skiadas and C. H. Skiadas, Development, Simulation and Application of First Exit Time Densities to Life Table Data, Communications in Statistics 39, 444-451 (2010).

C. H. Skiadas and C. Skiadas, Exploring life expectancy limits: First exit time modelling, parameter analysis and forecasts, in Chaos Theory: Modeling, Simulation and Applications, C. H. Skiadas, I. Dimotikalis and C. Skiadas, Eds. (World Scientific,  Singapore), 357–368 (2011).

B. L. Strehler and A.S. Mildvan, General theory of mortality and aging, Science 132, 14-21 (1960).

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Figures from Life Expectance Estimates Program in Excel

 

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