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PLoS One. 2012;7(5):e37025. doi: 10.1371/journal.pone.0037025. Epub 2012 May 18.

A novel generalized normal distribution for human longevity and other negatively skewed data.

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  • 1Department of Biostatistics, University of Alabama at Birmingham, Birmingham, Alabama, United States of America. hrobertson@ms.soph.uab.edu


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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