mkhan
Full Member level 3
Dear Friends,
I have \[ n \] RVs, \[X_1, X_2, \cdots ,X_n\], each distributed normally with zero mean and (1/sqrt(2)) variance, so that Y = (X1)^2 + (X2)^2 + ... + (Xn)^2, and hence Y ~ \[\chi^{2}_{2n}\] . Now I sorted Y RVs in descending order so that I have Y1>Y2>...>Yn.
My question is that whether these sorted Ys follow the extreme value distribution (Gumbel) because Y1 is the extreme value or they will follow the Chi squared distribution of joint random variables Ys?
Your comments and suggestions are welcome.
MAK
I have \[ n \] RVs, \[X_1, X_2, \cdots ,X_n\], each distributed normally with zero mean and (1/sqrt(2)) variance, so that Y = (X1)^2 + (X2)^2 + ... + (Xn)^2, and hence Y ~ \[\chi^{2}_{2n}\] . Now I sorted Y RVs in descending order so that I have Y1>Y2>...>Yn.
My question is that whether these sorted Ys follow the extreme value distribution (Gumbel) because Y1 is the extreme value or they will follow the Chi squared distribution of joint random variables Ys?
Your comments and suggestions are welcome.
MAK