Over the years, measuring inequality based on the distribution of income has
been a major concern to economist. Inequality has had a broader concept than
poverty in that it is defined over the entire population not just for the portion
of the population below a certain poverty line. The Gini coefficient satisfy
many desirable properties of a good measure of inequality such as mean independence,
population size independence, symmetry, and Pigou-Dalton Transfer
sensitivity. The empirical observation (income) distribution exhibit excess
kurtosis and heavy tails. This research first described the probability distribution
of income. The study presented a proposed numerical integration method
to stochastic estimation of the Gini coefficient. The Proposed Numerical Integration
Method showed a better estimate of functions as compared to the
Newton’s cotes methods such as the Trapezium rule, Simpson’s 1/3 rule, Simpson’s
3/8 rule, Boole’s rule and Weddle’s rule. Diagnostic tests such as Q-Q
plots and Kolmogorov-Smirnov test were graphically and quantitatively used
to assess the fitness to the income data respectively. The study therefore concludes
that the proposed method is superior to the Newton-Cotes methods of
integration. Also, the Gini coefficient estimate using the proposed numerical
integration method with k=3 was 0.48 which shows that there is disparity in
income in Ghana and recommend to statisticians or mathematicians to use the
proposed numerical integration method when computing functions that can’t
be easily integrated.