Representations of the Generalized Pareto Distribution — pgpd • distionary

Representations of the Generalized Pareto Distribution

Usage

pgpd(q, location, scale, shape, lower.tail = TRUE)

qgpd(p, location, scale, shape)

dgpd(x, location, scale, shape)

Arguments

location: Location parameter to shift the GPD by.
scale: Scale parameter; single positive numeric.
shape: Shape parameter; single positive numeric. This is also the extreme value index, so that shape > 0 is heavy tailed, and shape < 0 is short-tailed.
lower.tail: Logical. If TRUE, cdf (default); if FALSE, survival function.
p: Vector of probabilities.
x, q: Vector of quantiles.

Value

Vector of evaluated GPD distribution.

Examples

pgpd(1:10, 0, 1, 1)
#>  [1] 0.5000000 0.6666667 0.7500000 0.8000000 0.8333333 0.8571429 0.8750000
#>  [8] 0.8888889 0.9000000 0.9090909
dgpd(1:10, 0, 2, 0)
#>  [1] 0.303265330 0.183939721 0.111565080 0.067667642 0.041042499 0.024893534
#>  [7] 0.015098692 0.009157819 0.005554498 0.003368973
qgpd(1:9 / 10, 2, 10, -2)
#> [1] 2.95 3.80 4.55 5.20 5.75 6.20 6.55 6.80 6.95