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

Published onAug 18, 2020
Bounded Power-law Characterizations of Solar Flares: A Maximum Product of Spacings Approach

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-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. NSF-REU solar physics program at SAO, grant number AGS-1850750


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