[R] Compute the Gini coefficient

[Erich Neuwirth]

> On 30 Mar 2016, at 02:53, Marine Regis <marine.regis at hotmail.fr> wrote:
> 
> Hello,
> 
> I would like to build a Lorenz curve and calculate a Gini coefficient in order to find how much parasites does the top 20% most infected hosts support.
> 
> Here is my data set:
> 
> Number of parasites per host:
> parasites = c(0,1,2,3,4,5,6,7,8,9,10)
> 
> Number of hosts associated with each number of parasites given above:
> hosts = c(18,20,28,19,16,10,3,1,0,0,0)
> 
> To represent the Lorenz curve:
> I manually calculated the cumulative percentage of parasites and hosts:
> 
> cumul_parasites <- cumsum(parasites)/max(cumsum(parasites))
> cumul_hosts <- cumsum(hosts)/max(cumsum(hosts))
> plot(cumul_hosts, cumul_parasites, type= "l”)


Your values in hosts are frequencies. So you need to calculate

cumul_hosts = cumsum(hosts)/sum(hosts)
cumul_parasites = cumsum(hosts*parasites)/sum(parasites)

The Lorenz curves starts at (0,0), so to draw it, you need to extend these vectors

cumul_hosts = c(0,cumul_hosts)
cumul_parasites = c(0,cumul_parasites)

plot(cumul_hosts,cum9l_parasites,type=“l”)


The Gini coefficient can be calculated as
library(reldist)
gini(parasites,hosts)


If you want to check, you can “recreate” the original data (number of parasited for each host) with

num_parasites = rep(parasites,hosts)

and
gini(num_parasites)

will also give you the Gini coefficient you want.



> 

>> From this Lorenz curve, how can I calculate the Gini coefficient with the function "gini" in R (package reldist) given that the vector "hosts" is not a vector of weights ?
> 
> Thank you very much for your help.
> Have a nice day
> Marine
> 
> 
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> 
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