2007/12/24 by G. Györgyi, G. Gyorgyi, N. R. Moloney +5 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Exponent #Extreme value theory #Financial Risk and Volatility Modeling #Geometry #Independent and identically distributed random variables #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Random variable #Renormalization #Renormalization group #Scaling #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.100.210601
4 pages, 3 figures
arxiv created 2007/12/24 · openalex publication_date 2008/05/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the deviations from the limit distributions in extreme value statistics arising 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. It is found 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.