Generalized Pareto severity

P(X > x) = (1 + xi (x - location) / beta)^(-1 / xi) above location. generalized_pareto_riegel(t, alpha_ini, alpha_tail) is Riegel's parameterization: local alpha alpha_ini at the threshold t, tending to alpha_tail far out. Properties: d@xi, d@beta, d@location. For tail estimation from draws, see gpd_fit().

Usage

generalized_pareto(xi, beta, location = 0, ptr = NULL)

generalized_pareto_riegel(t, alpha_ini, alpha_tail)

Arguments

xi

Shape.

beta

Scale; finite and positive.

location

Start of the support.

t

Threshold; finite and positive.

alpha_ini

Local alpha at t; positive.

alpha_tail

Local alpha far out; positive.

Value

A generalized_pareto object, which inherits from distribution.

Details

Supports the same operations as pareto.

Examples

g <- generalized_pareto_riegel(1000, 2, 1.5)
survival(g, 2000)
#> [1] 0.2805659
layer(g, 4000, 1000)
#> [1] 903.9604