Probability Distributions as Models for Mortality

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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 right-censoring 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. Forest Sci. 31:331-341.

Keywords: Negative binomial distribution; Richards function; Weibull distribution; gamma distribution

Document Type: Journal Article

Affiliations: Professor of Forestry and Statistics, School of Forest Resources, North Carolina State University, Box 8002, Raleigh, NC 27695-8002

Publication date: June 1, 1985

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