pgpd: Cumulative distribution of the Generalized Pareto...
In freakonometrics/TopIncomes: Estimation of Top Incomes Using Pareto Models

Description Usage Arguments Value See Also Examples

Cumulative distribution of the Generalized Pareto distribution (GPD)

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

`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

the c.d.f. of the Generalized Pareto distribution at points x,

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

(assuming xi non null). The expected value is then

E[X]=mu+beta/(1-xi)

dgpd, and rgpd

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