[R] Gini with frequencies

[Gabor Grothendieck]

On 6/24/05, Dimitri Joe <dimitrijoe at yahoo.com.br> wrote:
> Hi there,
> 
> I am trying to compute Gini coefficients for vectors containing income classes. The data I possess look loke this:
> 
> yit <- c(135, 164, 234, 369)
> piit <-  c(367, 884, 341, 74 )
> 
> where yit is the vector of income classes, and fit is the vector of associated frequencies.(This data is from Rustichini, Ichino and Checci (Journal of Public Economics, 1999) ). In ineq pacakge, Gini( ) doesn't seem to handle frequencies. On the other had, Lc() compute the Lorenz curve using these frequencies, but I don't manage to use its output to compute the Gini coefficient. I wonder if you have already writen some function to do this, or if you could shed some light here and help me.
> 

Assuming x and n as in the args to Lc, use Brown's formula:
	with(Lc(x,n), 1 - sum(diff(p) * (L[-1] + L[-length(L)])))
or equivalently:
	with(Lc(x,n), 1 - sum(c(0,diff(p),0) * (c(L,0) + c(0,L))))

See 
  http://en.wikipedia.org/wiki/Gini_coefficient
and the online inequality calculator which can be used to
double check results: 
  http://www.poorcity.richcity.org/calculator.htm