Statistical Models for Solar Flare Interval Distribution in Individual Active Regions

This article discusses statistical models for solar flare interval distribution in individual active regions. We analyzed solar flare data in 55 active regions that are listed in the Geosynchronous Operational Environmental Satellite (GOES) soft X-ray flare catalog for the years from 1981 to 2005. We discuss some problems with a conventional procedure to derive probability density functions from any data set and propose a new procedure, which uses the maximum likelihood method and Akaike Information Criterion (AIC) to objectively compare some competing probability density functions. Previous studies on solar flare interval distribution in individual active regions only dealt with constant or time-dependent Poisson process models, and no other models were discussed. We examine three models—exponential, lognormal, and inverse Gaussian—as competing models for probability density functions in this study. We found that lognormal and inverse Gaussian models are more likely models than the exponential model for solar flare interval distribution in individual active regions. Possible mechanisms of solar flare for the distribution models are briefly mentioned. We also investigated a time-dependence of probability density functions of solar flare interval distribution briefly, and found that some active regions show time-dependence for lognormal and inverse Gaussian distribution functions. The results suggest that solar flares do not occur randomly in time; rather, solar flare intervals appear to be regulated by solar flare mechanisms. Determining of a solar flare interval distribution is an essential step in probabilistic solar flare forecasting method in space weather research. We briefly mention a probabilistic solar flare forecasting method as an application of a solar flare interval distribution analysis. The application of our distribution analysis to a probabilistic solar flare forecasting method is one of the main objectives of this study.