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Flux distribution is an important tool to understand the variabilityprocesses in active galactic nuclei. We now have available a great deal ofobservational evidences pointing towards the presence of log-normal componentsin the high energy light curves, and different models have been proposed toexplain these data. Here, we collect some of the recent developments on thistopic using the well-known blazar Mrk 501 as example of complex and interestingaspects coming from its flux distribution in different energy ranges and atdifferent timescales. The observational data we refer to are those collected ina complementary manner by Fermi-LAT over multiple years, and by the First G-APDCherenkov Telescope (FACT) telescope and the H.E.S.S. array in correspondenceof the bright flare of June 2014.

Flux Distribution of Gamma-Ray Emission in Blazars: The Example of Mrk 501