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Table 5 Relative Error generated from the Gini coefficient using Trapezium, Simpson 1/3 and Simpson 3/8 numerical integration methods as compared with the exact estimation

From: Estimation of the Gini coefficient for the lognormal distribution of income using the Lorenz curve

Region/family head Trapezium Rule Simpson’s 1/3 Rule Simpson’s 3/8 Rule
Relative error (%) m Relative error (%) m Relative error (%) m
Greater Accra 5.931847 2 2.566260 2 3.407657 2
Eastern 6.136455 1 2.825999 2 4.158256 2
Ashanti 5.557793 2 3.302457 2 3.866291 2
Volta 5.250205 2 2.461034 2 3.855619 2
Western 2.205323 2 2.129278 2 2.167300 2
Brong Ahafo 16.47266 1 15.09700 1 15.73192 1
Central 3.269309 2 2.043318 2 2.411116 2
Northern 2.781899 2 0.556380 2 0.890208 2
Upper East 6.919105 1 3.476764 2 4.819277 2
Upper West 34.40672 1 3.605180 2 4.725236 2
Rural 2.131082 2 0.683554 2 0.804182 2
Urban 18.08899 1 6.874544 1 7.913931 1
Male head 4.25000 2 0.541667 2 0.791667 2
Female head 15.80064 1 6.415695 1 7.705903 1
All 10.49914 1 3.729203 2 4.532415 2