The main objective of the study is to compare different Newton-Cotes methods such as the
Trapezium rule, Simpson 1/3 rule and Simpson 3/8 rule to estimate the Gini coefficient of income.
Gini coefficient of income which is the most frequently used measure of income inequality
measures the variation among income distributions. Recently, there has been an increasing
practical and theoretical interest in the distribution of income and how to estimate the Lorenz curve
and Gini coefficient of income. Several researches in economics have been made on measurement
of income disparities among household or individual. There has been a few studies on numerical
integration methods used to estimate Lorenz curve and Gini coefficient specifically income, in
Africa and Ghana in particular. In this study we compare different Newton-Cotes methods in the
estimation of the Gini coefficient (GC); a summary statistics of Lorenz curve and a measure of
income inequality in a population. Specifically, we estimate the Lorenz curve by Newton-Cotes
methods namely the trapezium rule, Simpson’s 1/3 rule and Simpson’s 3/8 rule. And using these
curves we estimate the GC of income, and compare the accuracy of these estimates on some
(Ghanaian) data. We show that these rules give negative biases with the Trapezium rule yielding
the highest absolute relative error of 9.592007%.