Suppose we have $i$-th and $j$-th order statistics from a sample of i.i.d. random variables.
How to derive the difference between these order statistics? For example, it's obvious that, if $j>i$, then $F_j-F_i\geq0$. However, this does not apply to independent order statistics.
What would be the right way to find the distribution of $F_j-F_i$ provided that both values belong to the same sample?
P. S. I'm sorry if the question sounds awkward, my knowledge of probability theory is rather limited