Draft SGini

v <- c(8,5,1,3,5,6,7,6,3) # income
w <- seq(0.1, 0.9, 0.1) # weights


w <- w[order(v)]
v <- sort(v)


# compute πₖ

y <- unique(v)
pi_k <- purrr::map_dbl(split(w, v), sum)/sum(w)


# compute Fₖ

# F_k <- rep(0, length(pi_k))
# 
# for(i in 2:length(F_k)){
# 
#   F_k[i] <- F_k[i-1] + 0.5 * pi_k[i-1]
# 
# }


F_k <- c(cumsum(0.5 * pi_k))

mean(F_k)