  Many cosmological models of GRBs envision the energy source to be a
cataclysmic stellar event leading to a relativistically expanding fireball.
Particles are thought to be accelerated at shocks and produce nonthermal
radiation. The highly variable temporal structure observed in most GRBs has
significantly constrained models. By using different methods of statistical
analysis in the time domain we find that the width of the large amplitude
pulses in GRB time histories remain remarkably constant throughout the classic
GRB phase. This is also true for small amplitude pulses. However, small and
large pulses do not have the same pulse width within a single time history. We
find a quantitative relationship between pulse amplitude and pulse width: the
smaller amplitude peaks tend to be wider, with amplitude following a power law
with an index of about -2.8. Internal shocks simulated by randomly selecting
the Lorentz factor and energy per shell are consistent with a power law
relationship. This is strong quantitative evidence that GRBs are, indeed,
caused by internal shocks. The dependency of the width-vs.-intensity
relationship on the maximum Lorentz factor provides a way to estimate that
elusive parameter. Our observed power law index indicates that \Gamma_{max} is
less or equal than 10^3. We also interpret the narrowness of the pulse width
distribution as indicating that the emission, that occurs when one shell over
takes another, is produced over a small range of distances from the central
site.
