TITLE:
Fitness of Four-Parameter Beta Distribution Function for Forecasting Gold Reserve and Its Production Lifespan in Ghana
AUTHORS:
Samuel Kwaku Obeng, Christiana C. Nyarko, Lewis Brew, K. Sagary Nokoe
KEYWORDS:
Gold Reserve, Four-Parameter Beta Distribution Function, Goodness of Fit Statistics
JOURNAL NAME:
Open Journal of Statistics,
Vol.13 No.4,
August
23,
2023
ABSTRACT: Ghana, renowned for its
abundant gold reserves, plays a significant role in the global mining industry.
Effective management and accurate forecasting of these reserves are vital for
sustainable resource utilization and economic planning. Forecasting gold
reserves and estimating their production lifespan are complex tasks that
require robust statistical models capable of capturing the underlying dynamics
of gold deposit accumulation and extraction. To this end, the four-parameter
Beta distribution function emerges as a promising candidate due to its flexibility
and ability to handle non-negative data. This research aims to investigate the
fitness and applicability of the four-parameter Beta distribution function for
forecasting Ghana’s gold reserves and estimating the production lifespan of
this precious resource. The empirical paper relied mainly on quarterly
secondary datasets on gold reserve between the years 2009 and 2022 secured from
the Minerals Commission of Ghana, Accra. Several known statistical
distributions including Beta, Weibull, Normal, Logistic and Gamma were explored
with Maximum Likelihood Estimation (MLE) and evaluated using model selection
criteria as AIC and BIC. Goodness of Fits were evaluated using
Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling
Statistic. Based on the analysis conducted, the four-parameter Beta
distribution provided the best fit for gold reserve in Ghana. At a 99.9%
confidence level and considering the current annual average gold production
estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of
gold production in Ghana extends to the year 1,953,765. This astounding
estimate suggests that the country’s gold reserves are expected to sustain
production for an extended period, providing a critical resource for economic
development and supporting the mining industry well into the distant future.