Extreme Value Analysis of Solar Energetic Proton Peak Fluxes

An extreme value analysis of >10 MeV solar proton event peak fluxes during the period 1967–1994 is carried out. The largest annual peak fluxes that exceed a few hundred cm–2 s–1 sr–1 are described by the type II extreme value distribution. One implication of this finding is that the extreme value distribution can be related to the initial distribution of large peak fluxes. Assuming that the number of events is a Poisson variable, the initial distribution is shown to be a power law with parameters that are directly related to the extreme value distribution parameters. The power law thus determined for the initial cumulative distribution has an index of –0.68, and agrees well with the data for peak fluxes above a few hundred cm–2 s–1 sr–1. Implications for using extreme value methods in conjunction with initial distributions that are represented by power laws are discussed.