Recently came across this question on how to find the xth percentile for a given stream of numbers. I have a basic understanding of how this could be achieved if the stream was relatively small (can be stored into memory, sorted and the xth value can be found) but I was wondering how the percentile could be approximated if the stream of numbers is fairly large and the number of numbers is unknown.
How to approximate the xth percentile for a large unknown quantity of number
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I think you could use Reservoir sampling to select uniformly
k
elements from the streamS
and then approximate xth percentile ofS
with the xth percentile of thesek
numbers.k
depends on how much memory do you have and how precise the approximation should be.EDIT
Here is a code example to test the solution:
The result is:
I got a pretty good approximation for every
x
i used and currently i don't see why it can't be suitable for your case.