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Table 2 Estimates of the area under the Lorenz curve using Trapezium, Simpson 1/3 and Simpson 3/8 numerical integration methods

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

Region Trapezium rule Simpson’s 1/3 rule Simpson’s 3/8 rule Exact integration
Greater Accra 0.2764 0.2684 0.2704 0.2623
Eastern 0.2675 0.2593 0.2626 0.2523
Ashanti 0.2655 0.2599 0.2613 0.2517
Volta 0.2690 0.2622 0.2656 0.2562
Western 0.2428 0.2426 0.2427 0.2370
Brong Ahafo 0.2632 0.2593 0.2611 0.2165
Central 0.2633 0.2603 0.2612 0.2553
Northern 0.2379 0.2319 0.2328 0.2304
Upper East 0.2296 0.2196 0.2235 0.2095
Upper West 0.3126 0.2246 0.2278 0.2143
Rural 0.2566 0.2530 0.2533 0.2513
Urban 0.2754 0.24465 0.2475 0.2258
Male head 0.2702 0.2613 0.2619 0.26
Female head 0.2618 0.23525 0.2389 0.2171
All 0.2660 0.2483 0.2504 0.23855