Application Of Numerical Integration To Stochastic Estimation Of The Gini Coefficient

ABSTRACT 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.