Peak energy-isotropic energy relation in the off-axis gamma-ray burst model

Using a simple uniform jet model of prompt emissions of gamma-ray bursts (GRBs), we reproduce the observed peak energy - isotropic energy relation. A Monte Carlo simulation shows that the low isotropic energy part of the relation is dominated by events viewed from off-axis directions, and the number of the off-axis events is about one-third of the on-axis emissions. We also compute the observed event rates of the GRBs, the X-ray - rich GRBs, and the X-ray flashes detected by High Energy Transient Explorer 2, and we find that they are similar.