dpareto1: Density of the Pareto 1 distribution

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

Description

Density of the Pareto 1 distribution

Usage

dpareto1(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 density of the Pareto 1 distribution at points x

f(x)=alpha*mu^alpha/x^(alpha+1)

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

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

See Also

ppareto1, qpareto1 and rpareto1

Examples

# density of a Pareto1(1,1.5) at point 2
dpareto1(2, 1, alpha=1.5)
0.265165
# expected value of a Pareto1(1,1.5)
integrate(function(x) x*dpareto1(x, 1, alpha=1.5),-Inf,Inf)
# theoretical expected value
1*(1.5)/(1.5-1)

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