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Variable \gama-ray emission from blazars, one of the most powerful classes ofastronomical sources featuring relativistic jets, is a widely discussed topic.In this work, we present the results of a variability study of a sample of 20blazars using \gama-ray (0.1--300~GeV) observations from Fermi/LAT telescope.Using maximum likelihood estimation (MLE) methods, we find that the probabilitydensity functions that best describe the $\gamma$-ray blazar flux distributionsuse the stable distribution family, which generalizes the Gaussiandistribution. The results suggest that the average behavior of the \gama-rayflux variability over this period can be characterized by log-stabledistributions. For most of the sample sources, this estimate leads to standardlog-normal distribution ($\alpha=2$). However, a few sources clearly displayheavy tail distributions (MLE leads to $\alpha<2$), suggesting underlyingmultiplicative processes of infinite variance. Furthermore, the light curveswere analyzed by employing novel non-stationarity and autocorrelation analyses.The former analysis allowed us to quantitatively evaluate non-stationarity ineach source -- finding the forgetting rate (corresponding to decay time)maximizing the log-likelihood for the modeled evolution of the probabilitydensity functions. Additionally, evaluation of local variability allows us todetect local anomalies, suggesting a transient nature of some of thestatistical properties of the light curves. With the autocorrelation analysis,we examined the lag dependence of the statistical behavior of all the$\{(y_t,y_{t+l})\}$ points, described by various mixed moments, allowing us toquantitatively evaluate multiple characteristic time scales and implyingpossible hidden periodic processes.

Gamma-ray Blazar variability: New statistical methods of time-flux distributions