title: A novel generalized normal distribution for human longevity and other negatively skewed data.
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.
authors.affiliation: Department of Biostatistics, University of Alabama at Birmingham, Birmingham, Alabama, United States of America. hrobertson@ms.soph.uab.edu
authors.forename: Henry T
authors.initials: HT
authors.lastname: Robertson
authors.forename: David B
authors.initials: DB
authors.lastname: Allison
mesh_terms: D000367:Age Factors; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016018:Least-Squares Analysis; D015993:Life Tables; D008136:Longevity / Q000502:physiology*; D008954:Models, Biological; D016011:Normal Distribution