We present a statistical characterization of the $gamma$-ray emission from the 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 time integration of 3-days between August 2008 - October 2015. The observed flux variation is large, spanning $gtrsim 2$ orders of magnitude between the extremes except for Mrk~421. We compute the flux distributions and compare with Gaussian and lognormal ones. We find that the 3 blazars have distribution consistent with a lognormal, suggesting that the variability is of a non-linear, multiplicative nature. This is further supported by the computation of 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 either by a lognormal or a Gaussian, while its flux-rms relation is still found to be linear. We also compute the power spectra, which suggest the presence of a break, but are consistent with typical scale-free power-law shot noise. The results are broadly consistent with the statistical properties of the magnetic reconnection powered minijets-in-a-jet model. We discuss other possible scenarios and implications of these observations on jet processes and connections with the central engine.
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