
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 13th, 2017, 01:59 PM  #1 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 107 Thanks: 0  Interpretation of Limiting Distribution
Let $X_1, ..., X_n$ be random variables independent and identically distributed on $Uniform(0,1)$. Let $X_{(n)}=MAX{(X_1,...,X_2)}$. Define $W_n=n(1X_{(n)})$. Find the limiting distribution of $W_n$ as $n$ increases without bound. Can you identify this limiting distribution? Give an interpretation of the result obtained above. So, I managed to find that the limiting distribution follows an exponential distribution with mean 1. However, I'm not quite sure how to "interpret" this. What's so special about $W_n$ that makes this result significant when $n$ grows large? 
December 13th, 2017, 04:56 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,691 Thanks: 859 
I get that $f_{W_{(n)}}(w) = \left(1  \dfrac w n \right)^{n1},~w \in [0,n]$ $\lim \limits_{n\to\infty}~f_{W_{(n)}}(w) = e^{w},~w \in [0,\infty)$ 
December 13th, 2017, 05:18 PM  #3 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 107 Thanks: 0 
Right, that's exactly what I found; it's exponential with mean 1. But the real question here is: how do you "interpret" that? 

Tags 
distribution, interpretation, limiting 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Interpreting the limiting distribution of markov chains?  Keroro  Advanced Statistics  0  June 14th, 2016 04:29 PM 
Interpretation of N(.) cumulative distribution function  Aqil  Advanced Statistics  0  March 9th, 2013 11:13 AM 
Limiting Distribution  problem  Advanced Statistics  1  November 2nd, 2009 02:36 PM 
limiting distribution  illusion  Advanced Statistics  0  December 4th, 2007 12:32 PM 
Limiting Distribution  illusion  Advanced Statistics  0  December 4th, 2007 12:28 PM 