×

Knowledge elicitation of Gompertz’ law of mortality. (English) Zbl 0971.62073

The paper deals with the Gompertz distribution which is rather widely used for modelling of dying out processes. The authors present explicit formulas for the moment generating function of the Gompertz law as well as for the mean and variance of this law. After reparametrization of the Gompertz law to a distribution with mean and variance parameters these explicit formulas lead to rather simple parameter estimators. Also a formula for the remaining life time is derived. Using the theory of heterogeneous populations, mortality models not only age dependent but also depending on summarizing risk factors are investigated.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62E15 Exact distribution theory in statistics
62F10 Point estimation
91D20 Mathematical geography and demography
92D25 Population dynamics (general)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Abramowitz M., Handbook of mathematical functions (1955)
[2] Benjamin B., The analysis of mortality and other actuarial statistics (1980)
[3] Cox D. R., Journal of the Statistical Society Series B 34 pp 506– (1972)
[4] Cox D. R., Analysis of survival data (1984)
[5] Gompertz, B. 1825.On the nature of the function expressive of the Law of Human Mortality and on a new mode of determining the Value of Life Contingencies, Philosophical Transactions, Royal Society, Vol. 36, 513–585. London: W. Nicol. [Gom l825]
[6] DOI: 10.2307/2061656
[7] Reiss R. D., Statistical analysis of extreme values (1997) · Zbl 0880.62002
[8] Mathai A. M., Generalized hypergeometric functions with applications in statistics and physical sciences (1973) · Zbl 0272.33001
[9] Vaupel J. W., Research report RR-83-1, in: The deviant dynamics of death in heterogeneous populations (1983)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.