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We study the possible effects of selection biases on the  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  E  peak  and the isotropic luminosity  L  iso , we are unable to reproduce it due to the flux limit threshold of the  Swift  complete sample. We can reject the null hypothesis that there is no intrinsic correlation between  E  peak  and  L  iso  at more than 2.7σ 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 1.6σ, the possibility that the observed  E  peak – L  iso  correlation among different bursts is caused by a boundary, i.e. such that for any given  E  peak , we see only the largest  L  iso , which has a flux above the threshold of the current instruments.

The impact of selection biases on the correlation of gamma‐ray bursts