  The observed log-normal flux distributions in the high energy emission from
blazars have been interpreted as being due to variability stemming from
non-linear multiplicative processes generated dynamically from the accretion
disc. On the other hand, rapid minute scale variations in the flux point to a
compact emitting region inside the jet, probably disconnected from the disc. In
this work, we show that linear Gaussian variations of the intrinsic particle
acceleration or escape time-scales can produce distinct non-Gaussian flux
distributions, including log-normal ones. Moreover, the spectral index
distributions can provide confirming evidence for the origin of the
variability. Thus, modelling of the flux and index distributions can lead to
quantitative identification of the micro-physical origin of the variability in
these sources. As an example, we model the X-ray flux and index distribution of
Mkn 421 obtained from over 9 years of MAXI observations and show that the
variability in the X-ray emission is driven by Gaussian fluctuations of the
particle acceleration process rather than that of the escape rate.
