  A classical model based on a power law assumption for the radius-time
relationship in the expansion of a Supernova (SN) allows to derive an
analytical expression for the flow of mechanical kinetic energy and the time
duration of Gamma-ray burst (GRB). A random process based on the ratio of two
truncated lognormal distributions for luminosity and luminosity distance allows
to derive the statistical distribution for time duration of GRBs. The high
velocities involved in the first phase of expansion of a SN requires a
relativistic treatment. The circumstellar medium is assumed to follow a density
profile of Plummer type with eta=6. A series solution for the relativistic flow
of kinetic energy allows to derive in a numerical way the duration time for
GRBs. Here we analyse two cosmologies: the standard cosmology and the plasma
cosmology.
