A Conjecture on Demographic Mortality Implies Two Asymptotic Limits for Mortality Curves in Demographic Life Tables

Giuseppe Alberti

doi:doi:10.11648/j.hss.20251306.14

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A Conjecture on Demographic Mortality Implies Two Asymptotic Limits for Mortality Curves in Demographic Life Tables

Giuseppe Alberti^*

Published in Humanities and Social Sciences (Volume 13, Issue 6)

Received: 25 October 2025 Accepted: 19 November 2025 Published: 11 December 2025

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Abstract

In a previous article, the author presented a conjecture on the trend of demographic mortality as life span progresses. This earlier article provided a mathematical formulation of the statistical distribution to which mortality would tend in this case. In the present work we show that this theory predicts that the height of the mortality peak with respect to demographic age and the amplitude at mid-height of the mortality curve itself are limited to fixed values, towards which the mortality curves will tend as the lifespan increases. These limit values are also calculated numerically. These limiting requirements derive directly from the mathematical formulation of the above said conjecture. Demographic data from the United States, Japan and Italy were used as an experimental test. For the Italian case in particular, regional subdivisions were also analyzed to see if any counterexamples to the assumed limits could emerge. In all cases, the assumed limits were not exceeded by the actual data and the apparent asymptotic trend towards these limits was confirmed by the collected data. The identified height limit also gives us a quick test for future Life Tables with 5-year age intervals: the dx data for them, in the maximum mortality interval, may not exceed 29.3% of the total cases.

Published in	Humanities and Social Sciences (Volume 13, Issue 6)
DOI	10.11648/j.hss.20251306.14
Page(s)	548-556
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Demographic Mortality, Life Tables, Statistical Distribution, Statistical Mechanics, Cellular Automata, Lifespan

References

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[2]	W. M. Makeham, On the Law of Mortality and the Construction of Annuity Tables, in J. Inst. Actuaries and Assur. Mag., vol. 8, 1860, pp. 301-310.
[3]	Lee, Ronald D.; Carter, Lawrence R. (September 1992). "Modeling and Forecasting U.S. Mortality". Journal of the American Statistical Association. 87(419): 659-671. https://doi.org/10.2307/2290201
[4]	D. Makowiec, D. Stauffer and M. Zieliński, “Gompertz law in simple computer model of ageing of biological population”, http://arxiv.org/abs/cond-mat/0107107v1
[5]	A. Racco, M. Argollo de Menezes and T. J. Penna “Search for an unitary mortality law through a theoretical model for biological ageing”, http://arxiv.org/abs/adap-org/9709002v1
[6]	M. D. Pascariu, A. Lenart & V. Canudas-Romo (2019) “The maximum entropy mortality model: forecasting mortality using statistical moments”, Scandinavian Actuarial Journal, 2019: 8, 661-685, https://doi.org/10.1080/03461238.2019.1596974
[7]	A. Boulougari, K. Lundengård, M. Rančić, S.Silvestrov, S. Suleiman & B. Strass (2019) “Application of a power-exponential function-based model to mortality rates forecasting”, Communications in Statistics: Case Studies, Data Analysis and Applications, 5: 1, 3-10, https://doi.org/10.1080/23737484.2019.1578705
[8]	S. J. Clark “A General Age-Specific Mortality Model With an Example Indexed by Child Mortality or Both Child and Adult Mortality”, Demography. 2019 June; 56(3): 1131-1159. https://doi.org/10.1007/s13524-019-00785-3
[9]	L. A. Gavrilov and N. S. Gavrilova, "The Reliability Theory of Aging and Longevity" J. theor. Biol. (2001) 213, 527-545.
[10]	P. Y. Nielsen, M. K Jensen, N. Mitarai, S. Bhatt “The Gompertz Law emerges naturally from the inter dependencies between sub components in complex organisms” https://doi.org/10.1038/s41598-024-51669-5
[11]	G. Alberti, “A conjecture on demographic mortality at high ages”. https://doi.org/10.48550/arXiv.2307.10279
[12]	G. Alberti “Fermi statistics method applied to model macroscopic demographic data”. https://doi.org/10.48550/arXiv.2205.12989
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[14]	L. A. Gavrilov and N. S. Gavrilova, "Mortality Measurement at Advanced Ages: a Study of the Social Security Administration Death Master File”, North American Actuarial Journal. 15(3): 432-447. https://doi.org/10.1080/10920277.2011.10597629
[15]	Elizabeth Arias and Jiaquan Xu, “United States Life Tables, 2017", NVSS, Volume 68, Number 7, June 24, 2019.
[16]	National Institute of Population and Social Security, “The Japanese Mortality Database”, Available from: HYPERLINK "https://www.ipss.go.jp/p-toukei/JMD/index-en.asp" https://www.ipss.go.jp/p-toukei/JMD/index-en.asp [Accessed 13 November 2025]
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APA Style

Alberti, G. (2025). A Conjecture on Demographic Mortality Implies Two Asymptotic Limits for Mortality Curves in Demographic Life Tables. Humanities and Social Sciences, 13(6), 548-556. https://doi.org/10.11648/j.hss.20251306.14

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ACS Style

Alberti, G. A Conjecture on Demographic Mortality Implies Two Asymptotic Limits for Mortality Curves in Demographic Life Tables. Humanit. Soc. Sci. 2025, 13(6), 548-556. doi: 10.11648/j.hss.20251306.14

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AMA Style

Alberti G. A Conjecture on Demographic Mortality Implies Two Asymptotic Limits for Mortality Curves in Demographic Life Tables. Humanit Soc Sci. 2025;13(6):548-556. doi: 10.11648/j.hss.20251306.14

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@article{10.11648/j.hss.20251306.14,
  author = {Giuseppe Alberti},
  title = {A Conjecture on Demographic Mortality Implies Two Asymptotic Limits for Mortality Curves in Demographic Life Tables},
  journal = {Humanities and Social Sciences},
  volume = {13},
  number = {6},
  pages = {548-556},
  doi = {10.11648/j.hss.20251306.14},
  url = {https://doi.org/10.11648/j.hss.20251306.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.hss.20251306.14},
  abstract = {In a previous article, the author presented a conjecture on the trend of demographic mortality as life span progresses. This earlier article provided a mathematical formulation of the statistical distribution to which mortality would tend in this case. In the present work we show that this theory predicts that the height of the mortality peak with respect to demographic age and the amplitude at mid-height of the mortality curve itself are limited to fixed values, towards which the mortality curves will tend as the lifespan increases. These limit values are also calculated numerically. These limiting requirements derive directly from the mathematical formulation of the above said conjecture. Demographic data from the United States, Japan and Italy were used as an experimental test. For the Italian case in particular, regional subdivisions were also analyzed to see if any counterexamples to the assumed limits could emerge. In all cases, the assumed limits were not exceeded by the actual data and the apparent asymptotic trend towards these limits was confirmed by the collected data. The identified height limit also gives us a quick test for future Life Tables with 5-year age intervals: the dx data for them, in the maximum mortality interval, may not exceed 29.3% of the total cases.},
 year = {2025}
}

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TY  - JOUR
T1  - A Conjecture on Demographic Mortality Implies Two Asymptotic Limits for Mortality Curves in Demographic Life Tables
AU  - Giuseppe Alberti
Y1  - 2025/12/11
PY  - 2025
N1  - https://doi.org/10.11648/j.hss.20251306.14
DO  - 10.11648/j.hss.20251306.14
T2  - Humanities and Social Sciences
JF  - Humanities and Social Sciences
JO  - Humanities and Social Sciences
SP  - 548
EP  - 556
PB  - Science Publishing Group
SN  - 2330-8184
UR  - https://doi.org/10.11648/j.hss.20251306.14
AB  - In a previous article, the author presented a conjecture on the trend of demographic mortality as life span progresses. This earlier article provided a mathematical formulation of the statistical distribution to which mortality would tend in this case. In the present work we show that this theory predicts that the height of the mortality peak with respect to demographic age and the amplitude at mid-height of the mortality curve itself are limited to fixed values, towards which the mortality curves will tend as the lifespan increases. These limit values are also calculated numerically. These limiting requirements derive directly from the mathematical formulation of the above said conjecture. Demographic data from the United States, Japan and Italy were used as an experimental test. For the Italian case in particular, regional subdivisions were also analyzed to see if any counterexamples to the assumed limits could emerge. In all cases, the assumed limits were not exceeded by the actual data and the apparent asymptotic trend towards these limits was confirmed by the collected data. The identified height limit also gives us a quick test for future Life Tables with 5-year age intervals: the dx data for them, in the maximum mortality interval, may not exceed 29.3% of the total cases.
VL  - 13
IS  - 6
ER  -

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Author Information

Giuseppe Alberti

Independent Researcher, Como, Italy

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http://orcid.org/0000-0002-3041-8016

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APA Style

Alberti, G. (2025). A Conjecture on Demographic Mortality Implies Two Asymptotic Limits for Mortality Curves in Demographic Life Tables. Humanities and Social Sciences, 13(6), 548-556. https://doi.org/10.11648/j.hss.20251306.14

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ACS Style

Alberti, G. A Conjecture on Demographic Mortality Implies Two Asymptotic Limits for Mortality Curves in Demographic Life Tables. Humanit. Soc. Sci. 2025, 13(6), 548-556. doi: 10.11648/j.hss.20251306.14

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AMA Style

Alberti G. A Conjecture on Demographic Mortality Implies Two Asymptotic Limits for Mortality Curves in Demographic Life Tables. Humanit Soc Sci. 2025;13(6):548-556. doi: 10.11648/j.hss.20251306.14

Copy | Download

@article{10.11648/j.hss.20251306.14,
  author = {Giuseppe Alberti},
  title = {A Conjecture on Demographic Mortality Implies Two Asymptotic Limits for Mortality Curves in Demographic Life Tables},
  journal = {Humanities and Social Sciences},
  volume = {13},
  number = {6},
  pages = {548-556},
  doi = {10.11648/j.hss.20251306.14},
  url = {https://doi.org/10.11648/j.hss.20251306.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.hss.20251306.14},
  abstract = {In a previous article, the author presented a conjecture on the trend of demographic mortality as life span progresses. This earlier article provided a mathematical formulation of the statistical distribution to which mortality would tend in this case. In the present work we show that this theory predicts that the height of the mortality peak with respect to demographic age and the amplitude at mid-height of the mortality curve itself are limited to fixed values, towards which the mortality curves will tend as the lifespan increases. These limit values are also calculated numerically. These limiting requirements derive directly from the mathematical formulation of the above said conjecture. Demographic data from the United States, Japan and Italy were used as an experimental test. For the Italian case in particular, regional subdivisions were also analyzed to see if any counterexamples to the assumed limits could emerge. In all cases, the assumed limits were not exceeded by the actual data and the apparent asymptotic trend towards these limits was confirmed by the collected data. The identified height limit also gives us a quick test for future Life Tables with 5-year age intervals: the dx data for them, in the maximum mortality interval, may not exceed 29.3% of the total cases.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - A Conjecture on Demographic Mortality Implies Two Asymptotic Limits for Mortality Curves in Demographic Life Tables
AU  - Giuseppe Alberti
Y1  - 2025/12/11
PY  - 2025
N1  - https://doi.org/10.11648/j.hss.20251306.14
DO  - 10.11648/j.hss.20251306.14
T2  - Humanities and Social Sciences
JF  - Humanities and Social Sciences
JO  - Humanities and Social Sciences
SP  - 548
EP  - 556
PB  - Science Publishing Group
SN  - 2330-8184
UR  - https://doi.org/10.11648/j.hss.20251306.14
AB  - In a previous article, the author presented a conjecture on the trend of demographic mortality as life span progresses. This earlier article provided a mathematical formulation of the statistical distribution to which mortality would tend in this case. In the present work we show that this theory predicts that the height of the mortality peak with respect to demographic age and the amplitude at mid-height of the mortality curve itself are limited to fixed values, towards which the mortality curves will tend as the lifespan increases. These limit values are also calculated numerically. These limiting requirements derive directly from the mathematical formulation of the above said conjecture. Demographic data from the United States, Japan and Italy were used as an experimental test. For the Italian case in particular, regional subdivisions were also analyzed to see if any counterexamples to the assumed limits could emerge. In all cases, the assumed limits were not exceeded by the actual data and the apparent asymptotic trend towards these limits was confirmed by the collected data. The identified height limit also gives us a quick test for future Life Tables with 5-year age intervals: the dx data for them, in the maximum mortality interval, may not exceed 29.3% of the total cases.
VL  - 13
IS  - 6
ER  -

Copy | Download