Convergence of the empirical distribution to the poisson process
Ata N. Al-Hussaini, J. elliott Robert · Stochastics · 1984
A process associated with the empirical distribution of a family of positive i.i.d. random variables is shown to converge to a rate changed Poisson process when the distribution function is differentiable at zero. Furthermore, when the distribution function is differentiable in a neighbourhood of zero an estimate for the rate of convergence is obtained.