How to plot the Lorenz curve in R

I would like to plot Lorenz curve for the given pdf

L=function(x,a,l,b)
{
  term1=exp(-l*x-(b*x)^a)
  term2=a*l*(b*x)^a
  term3=a*b*(1+l)*((b*x)^(a-1))
  term4=(l^2)*(1+x)
  pdf=(term1/(1+l))*(term2+term3+term4)
  return(pdf)
}

Given a=l=b=1. Can anyone help to do this in R.

CDF is given by

Cdf=function(x,a,l,b)
{
  term5=(1+l+l*x)/(1+l)
  cdf=1-term5*term4
  return(cdf)
}

Your PDF is f(x) = e^(-2*x)/2 * (3+2*x). It is defined on (0, infinity) (I checked the integral with Wolfram). We will need its average which is 5/8 (=0.625) according to Wolfram.

Wolfram also provides the CDF (which is not the one you give):

F(x) = -e^(-2*x)/2 * (x+2) + 1.

Wolfram also provides the solution of F(x) = p, that is to say the quantile function. It is

Q(p) = -W(4*(p - 1)/e^4)/2 - 2 

where W is the Lambert W function.

Now we have to integrate Q. Again, Wolfram is successful:

Now we have everything needed.

library(lamW)
H0 <- function(p) { 
  u <- 4*(p - 1)/exp(4)
  (1 - p) * (lambertWm1(u)^2 - lambertWm1(u) + 1) / (2 * lambertWm1(u)) - 2*p
}
Lorenz <- function(p) {
  (H0(p) - H0(0)) / 0.625
}
curve(Lorenz(x), from = 0, to = 1)

This looks like a Lorenz curve.