dgpd: Density of the Generalized Pareto distribution (GPD)

In freakonometrics/TopIncomes: Estimation of Top Incomes Using Pareto Models

Description

Density of the Generalized Pareto distribution (GPD)

Usage

dgpd(x, xi = 1/alpha, alpha = 1/xi, mu = 0, beta = 1)

Arguments

x	numeric, (positive) vector
xi	numeric, inverse of alpha
alpha	numeric, tail index
mu	numeric, lower bound, default is 0
beta	numeric, scaling paramater, default = 1

Value

the density of the Pareto 1 distribution at points x,

f(x)=(1/beta)*(1+xi*(x-mu)/beta)^(-1/xi-1)

See Also

pgpd, and rgpd

Examples

dgpd(2, xi=1/1.5, 1, 1)
# expected value of a GPD(1,1.5,0,1)
integrate(function(x) x*dgpd(x,alpha=1.5,mu=0,beta=1),0,Inf)
integrate(function(x) x*dgpd(x,xi=1/1.5,mu=0,beta=1),0,Inf)
## theoretical value
0+1/(1-1/1.5)

freakonometrics/TopIncomes documentation built on July 7, 2019, 8:06 a.m.