Distribution of maximal distance between uniformly sampled variables

Hi everyone!

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

Hello,

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... :