Mean deviation about the mean, \(E|Z - \mu|\), or about the median.
Usage
bd_mean_deviation(a, b, c, k, about = c("mean", "median"), rel.tol = 1e-10)
Arguments
- a
Shape parameter (beta generator).
- b
Shape parameter governing the tail.
- c
Shape parameter (baseline).
- k
Scale parameter (baseline).
- about
`"mean"` (default) or `"median"`.
- rel.tol
Passed to [stats::integrate()].
Value
A single number, or `NA` when \(b \le 1\).
Details
\(E|Z - \mu| = 2\mu F(\mu) - 2 M_1(\mu)\) and
\(E|Z - M| = \mu - 2 M_1(M)\), with \(M\) the median.
Examples
bd_mean_deviation(a = 1.5, b = 3, c = 2, k = 1)
#> [1] 1.256399
bd_mean_deviation(a = 1.5, b = 3, c = 2, k = 1, about = "median")
#> [1] 1.138017