How do I calculate the probability for a given quantile in R?

Question

Using R, it is trivial to calculate the quantiles for given probabilities in a sampled distribution:

x <- rnorm(1000, mean=4, sd=2)
quantile(x, .9) # results in 6.705755

However, I can't find an easy way to do the inverse—calculate the probability for a given quantile in the sample x. The closest I've come is to use pnorm() with the same mean and standard deviation I used when creating the sample:

pnorm(5, mean=4, sd=2) # results in 0.6914625

However, because this is calculating the probability from the full normal distribution, and not the sample x, it's not entirely accurate.

Is there a function that essentially does the inverse of quantile()? Something that essentially lets me do the same thing as pnorm() but with a sample? Something like this:

backwards_quantile(x, 5)

I've found the ecdf() function, but can't figure out a way to make it result in a single probability instead of a full equation object.

Answer 1

ecdf returns a function: you need to apply it.

f <- ecdf(x)
f( quantile(x,.91) )
# Equivalently:
ecdf(x)( quantile(x,.91) )

Answer 2

Just for convenience, this function helps:

quantInv <- function(distr, value) ecdf(distr)(value)
set.seed(1)
x <- rnorm(1000, mean=4, sd=2)
quantInv(x, c(4, 5, 6.705755))
[1] 0.518 0.685 0.904