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

Table 5

Bonferroni index (𝐵) for given distributions.

Distribution	cdf	Bonferroni curve 𝐵(𝑝)	Bonferroni index (𝐵)
Exponential	1−𝑒^−𝜆𝑥,𝜆>0,𝑥≥0	𝑝+1−𝑝log(1−𝑝)𝑝	𝜋^26−1
Pareto	𝑥1−𝑥0^−𝛼,𝛼>1,𝑥≥𝑥0>0	1−(1−𝑝)^(𝛼−1)/𝛼𝑝	𝜓(2)()−𝜓𝛼−1𝛼
Power	𝑥^𝛼,𝛼>1,0≤𝑥≤1	𝑝^1/𝛼	1(𝛼+1)

Where 𝜓(𝑥) is the digamma function.