Comparative Study of Mathematical Models for Ghanaâ€™s Gold Production
Keywords:Sigmoid, Logistic, Gompertz, Gaussian, Probit, Hill, Gold
Sigmoid functions were used to approximate the cumulative gold production in Ghana. The functions examined were the logistic, Gompertz, Gaussian, Probit and the Hill, which were then used to predict into the future. Although all the five approximated models gave a good estimation of the reality, the Gompertz function was identified to give the best approximation of the observed trend of gold production in Ghana. The model was selected based on its high proportion of variance explained (R2 = 0.9402) as well as having the least value in terms of error (RMSE) and information loss (AIC). The model suggested that gold production could escalate to a level of 7040813 Oz in the future. It also showed that, industrial scale production of gold should be possible even after the year 2050 provided the current upward trend of gold production in Ghana continues.
Amankwah, R. K. and Suglo, R. S. (2003), â€œThe Trend of Gold Mining in Ghanaâ€, Ghana Mining Journal, Vol. 7, pp. 21-26.
Appiah, S. T., Wiah, E. N., Brew, L. and Kwateng, F, (2016), â€œComparative Study of Mathematical Models for Population Projectionâ€, 2nd UMaT Biennial International Mining and Mineral Conference, pp. 359-365.
Bliss, C. I. (1935), â€œThe calculation of the dosage-mortality curveâ€, Annals of Applied Biology, Vol. 22, pp.134â€“167.
Gbireh A. B., Cobblah A. and Suglo R. S. (2007), â€œAnalysis of the Trends of Gold Mining in Ghanaâ€, Ghana Mining Journal, Vol. 9, pp. 38-49.
Gompertz, B. (1825), â€œOn the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingenciesâ€, Philos. Trans. Roy. Soc., Vol. 123, pp. 513-585.
Goutelle, S., Maurin, M., Rougier, F., Barbaur, X., Bourguignon, L., Ducher, M. and Maire, P. (2008), â€œThe Hill equation: a review of its capabilities in pharmacological modellingâ€ Fundam. Clin. Pharm., Vol. 22, pp. 633-648.
Guo, H. (2011), A Simple Algorithm for Fitting a Gaussian Function, IEEE, Vol. 28, No. 5, pp. 134-137.
Hagen, N., Kupinski, M. and Dereniak, E. L. (2007), â€œGaussian profile estimation in one dimensionâ€, Appl. Opt., Vol. 46, pp. 5374-5383.
MÃ¼ller, J. And Dirner, V. (2010), â€œUsing Sigmoid Functions for Modelling South African Gold Productionâ€, GeoScience Engineering, Vol. LVI, No. 2, pp. 44-58.
Verhulst, P. F. (1838), â€œNotice sur la loi que la population suit dans son accroissementâ€, Corr. Math. Physics, Vol. 10, pp. 113-121.
Weiss, J. N. (1997), â€œThe Hill equation revisited: uses and misusesâ€, FASEB Journal, Vol. 11, No. 11, pp. 835-841.
Copyright Â© 2021 University of Mines and Technology (UMaT), Tarkwa. Ghana