  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.
