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

• Main Authors: Henry T Robertson, David B Allison
• Format: Article
• Language: English
• Published: Public Library of Science (PLoS) 2012-01-01
• Series: PLoS ONE
• Online Access: http://europepmc.org/articles/PMC3356396?pdf=render

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.