Inverse function of an unknown cumulative function

Question

I'm working with a data file, the observations inside are random values. In this case I don't know the distribution of x (my observations). I'm using the function density in order to estimate the density, because I must apply a kernel estimation.

T=density(datafile[,1],bw=sj,kernel="epanechnikov")

After this I must integrate this because I'm looking for a quantile (similar to VaR, 95%). For this I have 2 options:

ecdf()
quantile()

Now I have the value of the quantile 95, but this is the data estimated by kernel.

Is there a function which I can use to know the value of the quantile 95 of the original data?

I remark that this is a distribution unknown, for this I would like to imagine a non parametric method as Newton, like the one that is in SAS solve()

Answer 1

You can use quantile() for this. Here is an example using random data:

> data<-runif(1000)

> q<-quantile(data, .95)
> q
      95% 
0.9450324 

Here, the data is uniformly distributed between 0 and 1, so the 95th percentile is close to 0.95.

To perform the inverse transformation:

> ecdf(data)(q)
[1] 0.95