  Future detection of a supernova neutrino burst by large underground detectors
would give important information for the explosion mechanism of collapse-driven
supernovae. We studied the statistical analysis for the future detection of a
nearby supernova by using a numerical supernova model and realistic Monte-Carlo
simulations of detection by the Super-Kamiokande detector. We mainly discuss
the detectability of the signatures of the delayed explosion mechanism in the
time evolution of the $\anue$ luminosity and spectrum. For a supernova at 10
kpc away from the Earth, we find that not only the signature is clearly
discernible, but also the deviation of energy spectrum from the Fermi-Dirac
(FD) distribution can be observed. The deviation from the FD distribution
would, if observed, provide a test for the standard picture of neutrino
emission from collapse-driven supernovae. For the $D$ = 50 kpc case, the
signature of the delayed explosion is still observable, but statistical
fluctuation is too large to detect the deviation from the FD distribution. We
also propose a method for statistical reconstruction of the time evolution of
$\anue$ luminosity and spectrum from data, by which we can get a smoother time
evolution and smaller statistical errors than a simple, time-binning analysis.
This method is useful especially when the available number of events is
relatively small, e.g., a supernova in the LMC or SMC. Neutronization burst of
$\nu_e$'s produces about 5 scattering events when $D$ = 10 kpc and this signal
is difficult to distinguish from $\anue p$ events.
