How to show that the difference of two Gumbel distributed random variables makes a Logistic distribution?

NAGG

New member
Joined
Apr 19, 2021
Messages
3
How to show that, for two random variables X∼Gumbel[a,b] and Y∼Gumbel[c,b], X−Y∼Logistic[a-c,b]? Can anyone show step by step how to make solution? Thank you!
 

HallsofIvy

Elite Member
Joined
Jan 27, 2012
Messages
7,453
You might want to start by defining "Gumbel Distribution" and "Logistic Distribution".
 

NAGG

New member
Joined
Apr 19, 2021
Messages
3
You might want to start by defining "Gumbel Distribution" and "Logistic Distribution".
I know that for Logistic Distribution I have:
1618861118936.png

For Gumbel distribution I have:
1618861094728.png

I know that I need to get: F(x-y)=e^{x-y}/(1+e^{x-y}).
 
Top