Compute mean and desviaction of a Gumbel distribution of size N?

Questions
,
1

I find in a table that give for for N =10, the y (mean) and ? (deviation) for a GUMBEL (Extreme value I) (e.g: for N= 10, gives y?= 0.4952 ?= 0.9497) but

HOW it can be COMPUTE THE MEAN y? AND STANDARD DEVIATION ? OF GUMBEL VARIATE (y) VERSUS RECORD LENGTH (N) in Mathematica

Thanks a lot of
Guillermo

2

Based on Gumbel’s lectures the following function will reproduce the values in the table found here:

f[n_] := {n, Mean[Table[-Log[-Log[m/(n + 1)]], {m, 1, n}]] // N,
  StandardDeviation[Table[-Log[-Log[m/(n + 1)]], {m, 1, n}]] Sqrt[(n - 1)/n] // N}

For example:

f[10]
(* {10, 0.495207, 0.949625} *)