ppareto1: Cumulative distribution function of the Pareto 1 distribution

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

Description

Cumulative distribution function of the Pareto 1 distribution

Usage

ppareto1(x, mu = 1, alpha = 1/xi, xi = 1/alpha)

Arguments

x	numeric, (positive) vector
mu	numeric, lower bound, default is 1
alpha	numeric, tail index
xi	numeric, inverse of alpha

Value

the c.d.f. of the Pareto 1 distribution at points x

F(x)=1-(mu/x)^(alpha)

Expected value exists when alpha is larger than 1, and is

E[X]=alpha/(alpha-1)

See Also

dpareto1, qpareto1 and rpareto1

Examples

# probability to a Pareto1(1,1.5) to be smaller than 2
ppareto1(2, 1, 1.5)
0.6464466
# expected value of a Pareto1(1,1.5)
integrate(function(x) (1-ppareto1(x, 1, alpha=1.5)),0,Inf)
# theoretical expected value
1*(1.5)/(1.5-1)

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