Power-law distribution and scale-invariant structure from the first CHIME/FRB Fast Radio Burst catalog

We study the statistical property of fast radio bursts (FRBs) based on a selected sample of 190 one-off FRBs in the first CHIME/FRB catalog. Three power law models are used in the analysis, and we find the cumulative distribution functions of energy can be well fitted by bent power law and thresholded power law models. And the distribution functions of fluctuations of energy well follow the Tsallis $q$-Gaussian distribution. The $q$ values in the Tsallis $q$-Gaussian distribution are constant with small fluctuations for different temporal scale intervals, indicating a scale-invariant structure of the bursts. The earthquakes and soft gamma repeaters show similar properties, which are consistent with the predictions of self-organized criticality systems.