Probability distributions as models for mortality

Abstract

The necessary attributes for a mortality model for an even-aged forest stand are stated. The Weibull distribution, the gamma distribution, and the negative binomial distribution are proposed based on their previous use in failure research and as mortality models. A distribution derived from the Richards generalization of the von Bertalanffy growth equation is proposed. The four functions are examined mathematically and empirically using data from a loblolly pine spacing study to determine their usefulness as mortality models. The negative binomial distribution and its continuous analog, the gamma distribution, show instability under right-censoring and are computationally difficult. The Weibull distribution shows extreme instability under rightcensoring due to constraints on the location of the inflection points of its probability density function, limiting its value as a mortality model. The distribution derived from the Richards generalization of the von Bertalanffy function is stable under right-censoring, shows no constraints on assumable shapes, and is computationally simple.

Citation

Buford, M.A.; Hafley, W.L. 1985. Probability distributions as models for mortality. Forest Science: 31(2) 331-341. 11 p.