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

Table 6

Absolute Lorenz index (𝐴) for given distributions.

Distribution	cdf	Absolute Lorenz curve	Absolute Lorenz index (𝐴)
Exponential	1−𝑒^−𝜆𝑥,𝜆>0,𝑥≥0	1−𝑝log1−𝑝𝜆	14𝜆
Pareto	𝑥1−𝑥0^−𝛼,𝛼>1,𝑥≥𝑥0>0	𝛼𝑥01−𝑝1−1−𝑝^−1/𝛼(𝛼−1)	𝛼𝑥02(𝛼−1)(2𝛼−1)
Rectangular	𝑥−𝑎𝜃,𝑎≤𝑥≤𝑎+𝜃,𝜃>0,𝑎≥0	𝜃𝑝(𝑝−1)2	𝜃12