  We study the convergence and shape correction to the limit distributions of
extreme values due to the finite size (FS) of data sets. A renormalization
method is introduced for the case of independent, identically distributed (iid)
variables, showing that the iid universality classes are subdivided according
to the exponent of the FS convergence, which determines the leading order FS
shape correction function as well. We find that, for the correlated systems of
subcritical percolation and 1/f^alpha stationary (alpha<1) noise, the iid shape
correction compares favorably to simulations. Furthermore, for the strongly
correlated regime (alpha>1) of 1/f^alpha noise, the shape correction is
obtained in terms of the limit distribution itself.
