Let and . You can start from there:
.
This gives the distribution of .
Let be three independent, identically distributed and bounded random variables with density .
What is the distribution of: , as a function of ?
One can easily obtain the distribution of and . But how do you get the joint distribution?
Unless there is a better way to proceed.
Thanks in advance for your help.
It's in many books, Hogg and Craig for one.
I googled it the other day and I only found it online at another forum.
It was incorrect initially but someone finally fixed it.
sadly wikipedia only has this for uniforms...
http://en.wikipedia.org/wiki/Order_statistic
but from that you can see the full formula.
You can obtain the joint density of any subset of order stats directly.