We proposed a Hyperbolic Gompertz Growth Model
(HGGM), which was developed by introducing a shape parameter
(allometric). This was achieved by convoluting hyperbolic sine
function on the intrinsic rate of growth in the classical gompertz
growth equation. The resulting integral solution obtained
deterministically was reprogrammed into a statistical model and used
in modeling the height and diameter of Pines (Pinus caribaea). Its
ability in model prediction was compared with the classical gompertz
growth model, an approach which mimicked the natural variability of
height/diameter increment with respect to age and therefore provides
a more realistic height/diameter predictions using goodness of fit
tests and model selection criteria. The Kolmogorov Smirnov test and
Shapiro-Wilk test was also used to test the compliance of the error
term to normality assumptions while the independence of the error
term was confirmed using the runs test. 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
gompertz growth models better than the source model (classical
gompertz growth model) while the results of R2, Adj. R2, MSE and
AIC confirmed the predictive power of the Hyperbolic Gompertz
growth models over its source model.
 Richards, F. J. 1959: A flexible growth function for empirical use.
Journal of Experimental Botany 10: 290–300.
 Winsor, C. P 1932: The Gompertz curve as a growth curve. Proc.
National Academy of Science, 18, 1-8.
 Gompertz B 1825: On the nature of the function expressive of the law of
human mortality, and on a new mode of determining the value of life
contingencies. Phil Trans of the Royal Soc, 182:513-585.
 Oyamakin, S. O.; Chukwu, U. A.; and Bamiduro, T. A. 2013: On
Comparison of Exponential and Hyperbolic Exponential Growth Models
in Height/Diameter Increment of PINES (Pinuscaribaea)," Journal of
Modern Applied Statistical Methods: Vol. 12: Iss. 2, Article 24.Pp
 Oyamakin S. O., Chukwu A. U. 2014: On the Hyperbolic Exponential
Growth Model in Height/Diameter Growth of PINES (Pinuscaribaea),
International Journal of Statistics and Applications, Vol. 4 No. 2, 2014,
pp. 96-101. doi: 10.5923/j.statistics.20140402.03.
 Kansal AR, Torquato S, Harsh GR, 2000: Simulated brain tumor growth
dynamics using a three dimentional cellular automaton. J Theor Biol.,
 Draper, N.R. and H. Smith, 1981. Applied Regression Analysis. John
Wiley and Sons, New York
 Ratkowskay, D.A., 1983. Nonlinear Regression modeling. Marcel
Dekker, New York. 276p
 Marquardt, D.W., 1963. An algorithm for least squares estimation of
nonlinear parameters. Journal of the society for Industrial and Applied
Mathematics, 11: 431 – 441.
 Seber, G. A. F. and C. J. Wild, 1989. Nonlinear Regression. John Wiley
and Sons: NY
 Fekedulegn, D. 1996. Theoretical nonlinear mathematical models in
forest growth and yield modeling. Thesis, Dept. of Crop Science,
Horticulture and Forestry, University College Dublin, Ireland. 200p.
 Tabatabai M, Williams DK, Bursac Z. 2005: Hyperbolastic growth
models: Theory and application. TheorBiol Med Model, 2(14): 1-13.