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...
but from that you can see the full formula.
You can obtain the joint density of any subset of order stats directly.