How do I calculate the probability for a given quantile in R?
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
ecdf returns a function: you need to apply it.
f <- ecdf(x)
f( quantile(x,.91) )
# Equivalently:
ecdf(x)( quantile(x,.91) )