Bounded Power-law Characterizations of Solar Flares: A Maximum Product of Spacings Approach

Abstract:

We analyze the distributions of properties of solar flares in GOES and RHESSI databases covering cycles 23 and 24. These are typically distributed as power-laws over a wide range of values within a bounded region. Given this semi-parametric problem, we use the maximum product of spacings method to simultaneously estimate the left and right ends of the regions, normalization constants, and exponents of the power-laws. To find the error bars of the estimates, we perform a sensitivity analysis. We report results for several properties including total energy, peak flux, wait time, quiet time, and duration for the respective aggregate, by-solar cycle, and by-year distributions. For the first time, the exponents are estimated self-consistently over regions that are statistically demonstrated to follow a power-law. We confirm that the exponent for the total energy power-law is similar to previous estimates and does not exhibit a detectable trend over the past two cycles. Additionally, we find that the power-law steepens, as expected, for wait and quiet times as it gets closer to the solar maximas. This work is supported by the NSF-REU Solar Physics program at SAO, grant number AGS-1850750.