Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 9 5/6 2002 10.5194/npg-9-409-2002 http://www.nonlin-processes-geophys.net/9/409/2002/ http://www.nonlin-processes-geophys.net/9/409/2002/npg-9-409-2002.html http://www.nonlin-processes-geophys.net/9/409/2002/npg-9-409-2002.pdf 409 418 0000-00-00 Extremum statistics: a framework for data analysis S. C. Chapman G. Rowlands N. W. Watkins Physics Department, University of Warwick, Coventry CV4 7AL, UK British Antarctic Survey, High Cross, Madingley Rd., Cambridge CB3 0ET, UK Recent work has suggested that in highly correlated systems, such as sandpiles, turbulent fluids, ignited trees in forest fires and magnetization in a ferromagnet close to a critical point, the probability distribution of a global quantity (i.e. total energy dissipation, magnetization and so forth) that has been normalized to the first two moments follows a specific non-Gaussian curve. This curve follows a form suggested by extremum statistics, which is specified by a single parameter a (a = 1 corresponds to the Fisher-Tippett Type I ("Gumbel") distribution). Here we present a framework for testing for extremal statistics in a global observable. In any given system, we wish to obtain a, in order to distinguish between the different Fisher-Tippett asymptotes, and to compare with the above work. The normalizations of the extremal curves are obtained as a function of a. We find that for realistic ranges of data, the various extremal distributions, when normalized to the first two moments, are difficult to distinguish. In addition, the convergence to the limiting extremal distributions for finite data sets is both slow and varies with the asymptote. However, when the third moment is expressed as a function of a, this is found to be a more sensitive method.