A Brief Review on the Statistical Properties of Fast Radio Bursts

Abstract: Fast radio bursts (FRBs) are millisecond-duration radio transients of extragalactic origin, whose emission mechanisms and progenitors remain unresolved. Statistical analyses of the rapidly growing samples provide a promising means to constrain the underlying physics. In this review, we synthesize the statistical properties derived from current FRB catalogs, encompassing constraints on dispersion measure, redshift, energy/luminosity functions, repetition rate, and host-galaxy demographics. For repeating FRBs, we examine the statistics of energy, fluence/flux, waiting time, and discuss time-series analyses that reveal memory effects and chaotic dynamics. We further discuss the observational discovery and theoretical interpretation of periodic activity, and survey polarization properties that probe the magneto-ionic environments of FRB sources. Throughout, we emphasize robust empirical trends, account for observational biases and selection effects, and outline outstanding open questions regarding the physical origin of these enigmatic bursts.