Good morning. Please can you help me to solve this exercise?. I must to use limiting distribution and change of variable. Thank you my friend.
Let Yn denote the nth order statistic, with Yn=qXn:n – ln(n), of a random sample X1,X2,…………..Xn from a exponential distribution Xi~exp(q). Find the limiting distribution of Yn.
Isn't Xn:n the nth order stat, which is the max?
and then Yn=qXn:n – ln(n)?
Start with the distribution of the max, then make that basic transformation and look at the result.