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We present a statistical characterization of the $\gamma$-ray emission fromthe four \emph{Fermi}-LAT sources: FR I radio galaxy NGC 1275, BL Lac Mrk 421,FSRQs B2 1520+31 and PKS 1510-089 detected almost continuously over a timeintegration of 3-days between August 2008 - October 2015. The observed fluxvariation is large, spanning $\gtrsim 2$ orders of magnitude between theextremes except for Mrk~421. We compute the flux distributions and compare withGaussian and lognormal ones. We find that the 3 blazars have distributionconsistent with a lognormal, suggesting that the variability is of anon-linear, multiplicative nature. This is further supported by the computationof the flux-rms relation, which is observed to be linear for the 3 blazars.However, for NGC 1275, the distribution does not seem to be represented eitherby a lognormal or a Gaussian, while its flux-rms relation is still found to belinear. We also compute the power spectra, which suggest the presence of abreak, but are consistent with typical scale-free power-law shot noise. Theresults are broadly consistent with the statistical properties of the magneticreconnection powered minijets-in-a-jet model. We discuss other possiblescenarios and implications of these observations on jet processes andconnections with the central engine.

Gamma-ray Flux Distribution and Non-linear behavior of Four LAT Bright AGNs