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

Henry T Robertson and David B Allison

PLOS ONE, 2012, vol. 7, issue 5, 1-7

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.

Date: 2012
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0037025

DOI: 10.1371/journal.pone.0037025

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