  We have studied the statistics of giant pulses from the Crab pulsar for the
first time with particular reference to their widths. We have analyzed data
collected during 3.5 hours of observations conducted with the Westerbork
Synthesis Radio Telescope operated in a tied-array mode at a frequency of 1200
MHz. The PuMa pulsar backend provided voltage recording of X and Y linear
polarization states in two conjugate 10 MHz bands. We restricted the time
resolution to 4 microseconds to match the scattering on the interstellar
inhomogeneities. In total about 18000 giant pulses (GP) were detected in full
intensity with a threshold level of 6 sigma. Cumulative probability
distributions (CPD) of giant pulse energies were analyzed for groups of GPs
with different effective widths in the range 4 to 65 microseconds. The CPDs
were found to manifest notable differences for the different GP width groups.
The slope of a power-law fit to the high-energy portion of the CPDs evolves
from -1.7 to -3.2 when going from the shortest to the longest GPs. There are
breaks in the CPD power-law fits indicating flattening at low energies with
indices varying from -1.0 to -1.9 for the short and long GPs respectively. The
GPs with a stronger peak flux density were found to be of shorter duration. We
compare our results with previously published data and discuss the importance
of these peculiarities in the statistical properties of GPs for the heoretical
understanding of the emission mechanism responsible for GP generation.
