  Context. In the context of an in-depth understanding of GRBs and their
possible use in cosmology, some important correlations between the parameters
that describe their emission have been discovered, among which the "Ep,i-Eiso"
correlation is the most studied. Because of this, it is fundamental to shed
light on the peculiar behaviour of a few events, namely GRB 980425 and GRB
031203, that appear to be important outliers of the Ep,i-Eiso correlation.
Aims. In this paper we investigate if the locations of GRB 980425 and GRB
031203, the two (apparent) outliers of the correlation, may be due to an
observational bias caused by the lacking detection of the soft X-ray emissions
associated with these GRBs, from respectively the BATSE detector on-board the
Compton Gamma-Ray Observer and INTEGRAL, that were operating at the epoch of
the observations. We analyse the observed emission of other similar
sub-energetic bursts (GRBs 060218, 100316D and 161219B) observed by Swift and
whose integrated emissions match the Ep,i-Eiso relation. We simulate their
integrated and time-resolved emissions as would have been observed by the same
detectors that observed GRB 980425 and GRB 031203, aimed at reconstructing the
light curve and spectra of these bursts. Results. If observed by old generation
instruments, GRB 060218, 100316D and 161219B would appear as outliers of the
Ep,i-Eiso relation, while if observed with Swift or WFM GRB 060218 would
perfectly match the correlation. We also note that the instrument BAT alone
(15-150 keV) actually measured 060218 as an outlier. Conclusions. We suggest
that if GRB 980425 and GRB 031203 would have been observed by Swift and by eXTP
they may have matched the Ep,i-Eiso relation. This provides strong support to
the idea that instrumental biases can make some events in the lower-left corner
of the Ep,i-Eiso plane appearing as outliers of the "Amati relation".

High Energy Astrophysical Phenomena