  Phase diagram based on the mean square displacement (MSD) and the
distribution of diffusion coefficients of the time-averaged MSD for the
stored-energy-driven L\'evy flight (SEDLF) is presented. In the SEDLF, a random
walker cannot move while storing energy, and it jumps by the stored energy. The
SEDLF shows a whole spectrum of anomalous diffusions including subdiffusion and
superdiffusion, depending on the coupling parameter between storing time
(trapping time) and stored energy. This stochastic process can be investigated
analytically with the aid of renewal theory. Here, we consider two different
renewal processes, i.e., ordinary renewal process and equilibrium renewal
process, when the mean trapping time does not diverge. We analytically show the
phase diagram according to the coupling parameter and the power exponent in the
trapping-time distribution. In particular, we find that distributional behavior
of time-averaged MSD intrinsically appears in superdiffusive as well as normal
diffusive regime even when the mean trapping time does not diverge.
