The Application of the Random Time Transformation Method to Estimate Richards Model for Tree Growth Prediction

Óscar Cornejo (), Sebastián Muñoz-Herrera, Felipe Baesler and Rodrigo Rebolledo
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Óscar Cornejo: Departament of Industrial Engineering, Faculty of Engineering, Universidad Católica de la Santísima Concepción, Alonso de Ribera 2850, Concepcion 4090541, Chile
Sebastián Muñoz-Herrera: Departament of Industrial Engineering, Faculty of Engineering, Universidad Católica de la Santísima Concepción, Alonso de Ribera 2850, Concepcion 4090541, Chile
Felipe Baesler: Departament of Industrial Engineering, Faculty of Engineering, Universidad del Bio Bio, Avenida Ignacio Collao 1202, Concepcion 4051381, Chile
Rodrigo Rebolledo: Departament of Industrial Engineering, Faculty of Engineering, Universidad Católica de la Santísima Concepción, Alonso de Ribera 2850, Concepcion 4090541, Chile

Mathematics, 2023, vol. 11, issue 20, 1-19

Abstract: To model dynamic systems in various situations results in an ordinary differential equation of the form d y d t = g ( y , t , θ ) , where g denotes a function and θ stands for a parameter or vector of unknown parameters that require estimation from observations. In order to consider environmental fluctuations and numerous uncontrollable factors, such as those found in forestry, a stochastic noise process ϵ t may be added to the aforementioned equation. Thus, a stochastic differential equation is obtained: d Y t d t = f ( Y t , t , θ ) + ϵ t . This paper introduces a method and procedure for parameter estimation in a stochastic differential equation utilising the Richards model, facilitating growth prediction in a forest’s tree population. The fundamental concept of the approach involves assuming that a deterministic differential equation controls the development of a forest stand, and that randomness comes into play at the moment of observation. The technique is utilised in conjunction with the logistic model to examine the progression of an agricultural epidemic induced by a virus. As an alternative estimation method, we present the Random Time Transformation (RTT) method. Thus, this paper’s primary contribution is the application of the RTT method to estimate the Richards model, which has not been conducted previously. The literature often uses the logistic or Gompertz models due to difficulties in estimating the parameter form of the Richards model. Lastly, we assess the effectiveness of the RTT Method applied to the Chapman–Richards model using both simulated and real-life data.

Keywords: stochastic differential equations; Richards model; Random Time Transformation Technique; maximum likelihood estimate; growth models (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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