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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