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Finite-size scaling in extreme statistics
G Györgyi1, N R Moloney, K Ozogány
1Institute for Theoretical Physics-HAS, Eötvös University, Pázmány sétány 1/a, 1117 Budapest, Hungary.
Physical Review Letters
|June 4, 2008
Summary
Finite data set sizes cause deviations in extreme value statistics. A new renormalization method reveals that universality classes split based on convergence exponent, impacting shape corrections for various data types.
Area of Science:
- Statistical physics
- Extreme value theory
- Complex systems
Background:
- Extreme value statistics (EVS) describes the probability of rare events.
- Deviations from theoretical limit distributions occur with finite data sets.
- Understanding these finite-size effects is crucial for accurate statistical modeling.
Purpose of the Study:
- To investigate and quantify deviations from limit distributions in EVS caused by finite data set sizes.
- To introduce a renormalization method for analyzing these finite-size effects.
- To explore the impact of data correlations on shape corrections.
Main Methods:
- Development of a renormalization method for independent, identically distributed (iid) variables.
- Analysis of universality classes in EVS based on finite-size convergence exponents.
- Application and comparison with simulations for correlated systems (percolation, 1/f noise).
Main Results:
- Finite-size effects subdivide iid universality classes based on a convergence exponent.
- This exponent dictates the leading-order shape correction function.
- The derived iid shape correction shows good agreement with simulations for subcritical percolation and low-frequency (alpha<1) noise.
- For strongly correlated (alpha>1) 1/f noise, shape corrections are expressed using the limit distribution.
Conclusions:
- Finite data set size introduces quantifiable corrections to extreme value statistics.
- The convergence exponent offers a new way to classify universality classes in EVS.
- The developed method provides accurate predictions for shape corrections in both iid and correlated systems.
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