计算R中的收入和财富份额

Question

I have a simple question, but I am confused with how deciles, quantiles, percentiles are defined.

My purpose is to compute various income and wealth shares. That is the share of x% per cent of the population from total income or wealth.

So, say that one wants to compute how much wealth the top 10% own.

How I can do this on R? Are my below calculation correct?

MWE

w<-rgamma(10000, 3, scale = 1/3)

per <- quantile(w, c(0.1, 0.9))

top_1_percent <- (per[2]/sum(w))*100
bottom_90_percent <-per[1]/sum(w))*100

Answer 1

The top 10% should be:

sum(w[w > per[2]])/sum(w)

Alternately:

sum(tail(sort(w), .1 * length(w))) / sum(w)

The bottom 90% is 1 - top 10%.

Answer 2

If I understand the question correctly, the following will do it.

set.seed(1234)    # Make the results reproducible

w <- rgamma(10000, 3, scale = 1/3)
per <- quantile(w, c(0.1, 0.9))

Now get an index i1 on the top 10% and sum their wealth.

i1 <- w >= per[2]
sum(w[i1])
#[1] 2196.856

And the same for the bottom 10%, with index i2 .

i2 <- w <= per[1]
sum(w[i2])
#[1] 254.6375

Note that I am using >= and <= . See the help page ?quantile to see the types of quantile computations R can do. This is given by argument type .

Edit.

To compute proportions and percentages of wealth of the top 10% and bottom 10%, divide by the total wealth and multiply by 100 .

top10 <- sum(w[i1])/sum(w)
top10
#[1] 0.221291

100*top10
#[1] 22.1291

bottom10 <- sum(w[i2])/sum(w)
bottom10
#[1] 0.02564983

100*bottom10
#[1] 2.564983