Research Outputs

Now showing 1 - 2 of 2
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    Publication
    The application of the random time transformation method to estimate Richards model for tree growth prediction
    (MDPI, 2023) ;
    Cornejo-Zuñiga, Óscar
    ;
    Muñoz-Herrera, SebastiĂ¡n
    ;
    Baesler, Felipe
    To model dynamic systems in various situations results in an ordinary differential equation of the form dy/dt=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 ϵt may be added to the aforementioned equation. Thus, a stochastic differential equation is obtained: dYt/dt=f(Yt,t,θ)+ϵt. 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.
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    Publication
    EstimaciĂ³n de parĂ¡metros en modelos no lineales: Algoritmos y Aplicaciones
    (UNIVERSIDAD EIA, 2016) ;
    Cornejo-ZĂºĂ±iga, Ă“scar
    En este artĂ­culo se muestran diferentes algoritmos para estimar parĂ¡metros en modelos no lineales. Se aplican primeramente a una base de datos de problemas clasificados difĂ­ciles. Posteriormente, se muestra el comportamiento de los algoritmos para el estudio de crecimiento de la merluza comĂºn en machos y hembras, anchoveta y sardina comĂºn ajustando un modelo de Von Bertalanffy. Se aplica el test de Cerrato para la comparaciĂ³n de crecimientos entre gĂ©neros para la merluza comĂºn. Los algoritmos se implementaron en ambiente MATLAB presentando un buen comportamiento en cuanto a tiempo CPU, nĂºmero de iteraciones y exactitud de la soluciĂ³n encontrada respecto de valores certificados de los problemas de la base de datos.