On Differential Growth Equation to Stochastic Growth Model Using Hyperbolic Sine Function in Height/Diameter Modeling of Pines
Pure and Applied Mathematics Journal
Volume 3, Issue 5, October 2014, Pages: 99-104
Received: Sep. 15, 2014; Accepted: Sep. 30, 2014; Published: Oct. 10, 2014
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Authors
Oyamakin Samuel Oluwafemi, Dept. of Statistics, University of Ibadan, Ibadan, Oyo State, Nigeria
Chukwu Angela Unna, Dept. of Statistics, University of Ibadan, Ibadan, Oyo State, Nigeria
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Abstract
Richrads growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richards growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richards growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richards nonlinear growth models better than the classical Richards growth model.
Keywords
Height, Dbh, Forest, Pinus Caribaea, Hyperbolic, Richards, Stochastic
To cite this article
Oyamakin Samuel Oluwafemi, Chukwu Angela Unna, On Differential Growth Equation to Stochastic Growth Model Using Hyperbolic Sine Function in Height/Diameter Modeling of Pines, Pure and Applied Mathematics Journal. Vol. 3, No. 5, 2014, pp. 99-104. doi: 10.11648/j.pamj.20140305.12
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