Does anyone here have knowledge of extreme value theory in statistics or engineering?
I've recently learned that the maximum of a large number of independent, identically distributed normal random variables is a approximately distributed like the Gumbel distribution.
But I have not been able to find anywhere how to derive the parameters of that gumbel distribution from the mean and variance of the normal random variables whose maximum is being taken.
e.g.
If Xi are independent distributed Normal(mu , sigma^2) then max{X1, X2, X3, ... , X100000} is distributed Gumbel
But what are the parameters of that gumbel in terms of mu and sigma^2 ?
This is /tv/
We have waifus and memes
where in the last part of the post, mu is the mean of the Xi normal variables and sigma^2 is the variance of the Xi normal variables.
and the normal variables are i.i.d.
Well I know someone in my lab works on this sort of stuff.
Breh...
>>7666583
olivia wilde looks so different lately
>>7666578
Who is this sea moon daemon
>>7666763
some tumblr girl, the reverse image search should provide a name or url
please help with OP question
bump.
new picture to replace old OP picture that was deleted.
Please someone who is good at statistics respond.
if X1, ..., Xn are independent and Y = max{X1, ..., Xn} then the cumulative distribution function
P(Y <= y) = P(X1 <= y and X2 <= y and ... Xn <= y)
= P(X1 <= y) * P(X2 <= y) * ... * P(Xn <= y)
= P(X <= y)^n
can be easily expressed in terms of the normal CDF.
Then just differentiate both sides to recover the distribution function for Y.
