Extreme-Value Distribution Analysis of the Second CHIME/FRB Catalog: Assessing the Rarity of the One-off FRB 20250316A

Abstract

We present a statistical analysis of the extremely bright, apparently non-repeating fast radio burst FRB 20250316A, detected by the Canadian Hydrogen Intensity Mapping Experiment (CHIME), to assess its rarity. Using a model-agnostic framework based on the Generalized Extreme Value (GEV) distribution and the second CHIME/FRB catalog, we perform Bayesian fits to the block-maxima of its peak flux and fluence. Our analysis confirms FRB 20250316A as a pronounced statistical outlier in both quantities. For the peak flux, the best-fit GEV model follows an unbounded, heavy-tailed Fr\'echet-type distribution, yielding return periods of approximately $802$ years at the $68\%$ confidence level (CL), $81$ years at the $95\%$ CL, and $30$ years at the $99\%$ CL. The fluence distribution exhibits greater complexity: while the full sample is consistent with a Fr\'echet-type distribution (return period of approximately $55$, $15$, and $8$ years at the $68\%$, $95\%$ and $99\%$ CLs, respectively), removing three other conspicuous outliers reveals a light-tailed Weibull-type distribution with a finite upper bound that is far exceeded by the fluence of FRB 20250316A. Although its inferred recurrence time is shorter than that of the ``Brightest Of All Time'' (BOAT) gamma-ray burst GRB 221009A, FRB 20250316A represents a similarly exceptional event (a potential FRB ``BOAT'') within the relatively short observational baseline of wide-field radio surveys. This work affirms the existence of rare, extremely luminous events at the extreme upper end of the FRB luminosity distribution, which may delineate a distinct physical channel or the extreme tail of a complex luminosity function.