Distribution of maximal distance between uniformly sampled variables
I've got uniformly distributed iid random variables .
Then I sort them ( ).
My interest lies in
the distance between two adjacent values.
What I'd like to know is the distribution of . I'm working on a delta-encoding method (storing a sorted list by their differences indead of directly storing the values) and this would help me understand what values I can expect. So a decent approximation is good enough for me.
Thanks a lot!
Re: Distribution of maximal distance between uniformly sampled variables
Well I don't know about the approximation, but it's easy to get the pdf of Y if you're familiar with the change of variable transform for the pdf.
Otherwise, you could also do it this way, with conditional expectations (your question doesn't look like high school probability) :
it would approximately give this, with a suitable y... :