  [Zhang 2014] propose to redefine the true GRB central engine activity
duration, $t_{\rm burst}$, by considering the contributions from the prompt
$\gamma$-ray emission, X-ray flare and internal plateau features. With a
comprehensive study on a large sample of Swift GRBs, it is shown that the
$t_{\rm burst}$ distribution in the observer frame consists of a bimodal
feature, suggesting the existence of a new population of ultra-long GRBs. In
this work, we make a series of further studies on $t_{\rm burst}$: we update
the Swift GRB sample up to June 2016; we investigate the properties of $t_{\rm
burst}$ distribution in the rest frame; we redefine $t_{\rm burst}$ by
involving external plateau contributions; we make a multiple parameter analysis
to investigate whether the bursts within the ultra-long population being
statistically different in sense of other features besides the duration
distribution. We find that for all situations, the distribution of $t_{\rm
burst}$ requires two normal distributions in logarithmic space to provide a
good fit, both in observer frame and rest frame. Considering the observational
gap effect would not completely erase the bimodal distribution feature. However
the bursts within the ultra-long population may have no statistically different
in sense of other features besides the duration term. We thus suggest that if
the ultra-long population of GRBs indeed exists, their central engine mechanism
and radiation mechanism should be similar to the normal population, but they
have longer central engine activity timescale.
