Lorenz and Bonferroni Curves

Lorenz and Bonferroni Curves

Usage

bd_lorenz(p, a, b, c, k, rel.tol = 1e-10)

bd_bonferroni(p, a, b, c, k, rel.tol = 1e-10)

Arguments

p

Vector of probabilities in \([0, 1]\).

a

Shape parameter (beta generator).

b

Shape parameter governing the tail.

c

Shape parameter (baseline).

k

Scale parameter (baseline).

rel.tol

Passed to [stats::integrate()].

Value

A numeric vector the length of `p`.

Details

\(L(p) = M_1(Q(p))/\mu\) and \(B(p) = L(p)/p\), with \(Q\) the quantile function. Both require \(b > 1\).

Examples

p <- c(0.1, 0.25, 0.5, 0.75, 0.9)
bd_lorenz(p, a = 1.5, b = 3, c = 2, k = 1)
#> [1] 0.01546361 0.06131079 0.19138527 0.41544613 0.64418479
bd_bonferroni(p, a = 1.5, b = 3, c = 2, k = 1)
#> [1] 0.1546361 0.2452432 0.3827705 0.5539282 0.7157609