Quantiles Through Objective Function

#Quantiles

qexp(0.99,0.1)

## [1] 46.0517

#Quantiles with optim
#Discrete Simplified Case
n=10
Y <- c(1,2,3,4,5,6,7,8,9,10)
Finv <- function(aa){
    score <- 0
    for(cc in 1:n){
        obj <- function(cc){
            val <- 0
            for(i in Y){
                val[i] <- {if(i<cc){(aa-1)*(i-cc)} else{(aa)*(i-cc)}
                }
            }
        return(sum(val))}
    score[cc] <- obj(cc)
    }
score
plot(score)
    Quantile <- match(min(abs(score)),score)
    return(Quantile)
}
Finv(0.65) 

## [1] 7