N NAGG New member Joined Apr 19, 2021 Messages 3 Apr 19, 2021 #1 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!

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!

H HallsofIvy Elite Member Joined Jan 27, 2012 Messages 7,453 Apr 19, 2021 #2 You might want to start by defining "Gumbel Distribution" and "Logistic Distribution".

N NAGG New member Joined Apr 19, 2021 Messages 3 Apr 19, 2021 #3 HallsofIvy said: You might want to start by defining "Gumbel Distribution" and "Logistic Distribution". Click to expand... I know that for Logistic Distribution I have: For Gumbel distribution I have: I know that I need to get: F(x-y)=e^{x-y}/(1+e^{x-y}).

HallsofIvy said: You might want to start by defining "Gumbel Distribution" and "Logistic Distribution". Click to expand... I know that for Logistic Distribution I have: For Gumbel distribution I have: I know that I need to get: F(x-y)=e^{x-y}/(1+e^{x-y}).