Application of the Logistic, Gompertz, and Richards Growth Functions to Gentan Probability Analysis

In a previous paper, a stochastic model complying with a state-dependent growth rate function was proposed for Gentan probability estimation. The growth function applied was the so-called Mitscherlich type of growth function. In this paper, application of other growth functions, i.e., the logistic,...

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Bibliographic Details
Published in:Journal of forest research 2001-11, Vol.6 (4), p.265-272
Main Author: Yoshimoto, Atsushi
Format: Article
Language:English
Subjects:
forest management
Gentan probability
Probability
stochastic model
Stochastic models
Stochastic processes
Studies
time- and state-dependent growth dynamics
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Summary:In a previous paper, a stochastic model complying with a state-dependent growth rate function was proposed for Gentan probability estimation. The growth function applied was the so-called Mitscherlich type of growth function. In this paper, application of other growth functions, i.e., the logistic, Gompertz and Richards growth functions, is addressed. Assuming growth dynamics as a function of time and state, an alternative stochastic model is derived with the above three growth dynamics. In the proposed model, the time is assumed to be continuous and the state to be discrete. Like in the previous paper, the sum of the Gentan probabilities derived from the proposed model with three growth functions over time is proved to be always unity. This is because the state-dependent part of the growth dynamics is a linear function of the state, which is the same as in the Mitscherlich growth function. This leads to the binomial probability law for a stochastic process, satisfying the unity requirement of the sum of the Gentan probabilities.
ISSN:1341-6979
1610-7403
DOI:10.1007/BF02762467