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A Novel Generalized Normal Distribution for Human Longevity and other Negatively Skewed Data

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  • Henry T Robertson
  • David B Allison

Abstract

Negatively skewed data arise occasionally in statistical practice; perhaps the most familiar example is the distribution of human longevity. Although other generalizations of the normal distribution exist, we demonstrate a new alternative that apparently fits human longevity data better. We propose an alternative approach of a normal distribution whose scale parameter is conditioned on attained age. This approach is consistent with previous findings that longevity conditioned on survival to the modal age behaves like a normal distribution. We derive such a distribution and demonstrate its accuracy in modeling human longevity data from life tables. The new distribution is characterized by 1. An intuitively straightforward genesis; 2. Closed forms for the pdf, cdf, mode, quantile, and hazard functions; and 3. Accessibility to non-statisticians, based on its close relationship to the normal distribution.

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  • Henry T Robertson & David B Allison, 2012. "A Novel Generalized Normal Distribution for Human Longevity and other Negatively Skewed Data," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-7, May.
    • Handle: RePEc:plo:pone00:0037025
    DOI: 10.1371/journal.pone.0037025
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    References listed on IDEAS

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    1. Edwards Ryan D, 2009. "The Cost of Cyclical Mortality," The B.E. Journal of Macroeconomics, De Gruyter, vol. 9(1), pages 1-19, March.
    2. B. Devlin & Michael Daniels & Kathryn Roeder, 1997. "The heritability of IQ," Nature, Nature, vol. 388(6641), pages 468-471, July.
    3. Ishwaran H. & Takahara G., 2002. "Independent and Identically Distributed Monte Carlo Algorithms for Semiparametric Linear Mixed Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1154-1166, December.
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    Cited by:

    1. Ya-Hsuan Hu & Takeshi Emura, 2015. "Maximum likelihood estimation for a special exponential family under random double-truncation," Computational Statistics, Springer, vol. 30(4), pages 1199-1229, December.
    2. David de la Croix & Omar Licandro, 2015. "The longevity of famous people from Hammurabi to Einstein," Journal of Economic Growth, Springer, vol. 20(3), pages 263-303, September.
    3. Takeshi Emura & Ya-Hsuan Hu & Yoshihiko Konno, 2017. "Asymptotic inference for maximum likelihood estimators under the special exponential family with double-truncation," Statistical Papers, Springer, vol. 58(3), pages 877-909, September.
    4. Pablo Garcia-Sanchez & Olivier Pierrard, 2023. "Uncertain lifetime, health investment and welfare," BCL working papers 178, Central Bank of Luxembourg.
    5. Ahmed Hossain & Joseph Beyene, 2015. "Application of skew-normal distribution for detecting differential expression to microRNA data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 477-491, March.
    6. Jorge M. Uribe & Helena Chuliá & Montserrat Guillen, 2018. "Trends in the Quantiles of the Life Table Survivorship Function," European Journal of Population, Springer;European Association for Population Studies, vol. 34(5), pages 793-817, December.

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