Finite-size scaling in extreme statistics

Details Finite-size scaling in extreme statistics Finite-size scaling in extreme statistics

2007-12-24

arxiv.org/abs/0712.3993v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.100.210601

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.

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