  We study the possible effects of selection biases on the Ep-Liso correlation
caused by the unavoidable presence of flux-limits in the existing samples of
Gamma Ray Bursts (GRBs). We consider a well defined complete sample of Swift
GRBs and perform Monte Carlo simulations of the GRB population under different
assumptions for their luminosity functions. If we assume that there is no
correlation between the peak energy Ep and the isotropic luminosity Liso, we
are unable to reproduce it as due to the flux limit threshold of the Swift
complete sample. We can reject the null hypothesis that there is no intrinsic
correlation between Ep and Liso at more than 2.7 sigma level of confidence.
This result is robust against the assumptions of our simulations and it is
confirmed if we consider, instead of Swift, the trigger threshold of the Batse
instrument. Therefore, there must be a physical relation between these two
quantities. Our simulations seem to exclude, at a lower confidence level of 1.6
sigma, the possibility that the observed Ep-Liso correlation among different
bursts is caused by a boundary, i.e. such that for any given Ep, we see only
the largest Liso, which has a flux above the threshold of the current
instruments.
