  At present there are still several open questions about the origin of the
ultra high energy cosmic rays. However, great progress in this area has been
made in recent years due to the data collected by the present generation of
ground based detectors like the Pierre Auger Observatory and Telescope Array.
In particular, it is believed that the study of the composition of the cosmic
rays as a function of energy can play a fundamental role for the understanding
of the origin of the cosmic rays. The observatories belonging to this
generation are composed of arrays of surface detectors and fluorescence
telescopes. The duty cycle of the fluorescence telescopes is ~10 % in contrast
with the ~100 % of the surface detectors. Therefore, the energy calibration of
the events observed by the surface detectors is performed by using a
calibration curve obtained from a set of high quality events observed in
coincidence by both types of detectors. The advantage of this method is that
the reconstructed energy of the events observed by the surface detectors
becomes almost independent of simulations of the showers because just a small
part of the reconstructed energy, obtained from the fluorescence telescopes,
comes from simulations. However, the calibration curve obtained in this way
depends on the composition of the cosmic rays, which can introduce biases in
composition analyses when parameters with a strong dependence on primary energy
are considered. In this work we develop an analytical method to study these
effects. We consider AMIGA, the low energy extension of the Pierre Auger
Observatory corresponding to the surface detectors, to illustrate the use of
the method.
