Estimates of Inequality Indices Based on Simple Random, Ranked Set, and Systematic Sampling

Table 4

Gini index (𝐺) for given distributions.

Distribution	cdf	Lorenz curve 𝐿(𝑝)	Gini index (𝐺)
Exponential	1−𝑒^−𝜆𝑥,𝜆>0,𝑥≥0	𝑝+1−𝑝log(1−𝑝)	12
Pareto	𝑥1−𝑥0^−𝛼,𝛼>1,𝑥≥𝑥0>0	1−(1−𝑝)^(𝛼−1)/𝛼	1(2𝛼−1)
Power	𝑥^𝛼,𝛼>1,0≤𝑥≤1	𝑝^(𝛼+1)/𝛼	1(2𝛼+1)