  Context. Knowing the exact shape of the UV luminosity function of
high-redshift galaxies is important in order to understand the star formation
history of the early universe. However, the uncertainties, especially at the
faint and bright ends of the LFs, are still significant.
  Aims. In this paper, we study the UV luminosity function of redshift z = 2.5
- 4.5 galaxies in 2.38 deg^2 of ALHAMBRA data with I <= 24. Thanks to the large
area covered by ALHAMBRA, we particularly constrain the bright end of the
luminosity function. We also calculate the cosmic variance and the
corresponding bias values for our sample and derive their host dark matter halo
masses.
  Methods. We use a novel methodology based on redshift and magnitude
probability distribution functions (PDFs). This methodology robustly takes into
account the uncertainties due to redshift and magnitude errors, shot noise and
cosmic variance, and models the luminosity function in two dimensions (z; M_UV
).
  Results. We find an excess of bright ~ M*_UV galaxies as compared to the
studies based on broad-band photometric data. However, our results agree well
with the luminosity function of the magnitude-selected spectroscopic VVDS data.
We measure high bias values, b ~ 8 - 10, that are compatible with the previous
measurements considering the redshifts and magnitudes of our galaxies and
further reinforce the real high-redshift nature of our bright galaxies.
  Conclusions. We call into question the shape of the luminosity function at
its bright end; is it a double power-law as suggested by the recent broad-band
photometric studies or rather a brighter Schechter function, as suggested by
our multi-filter analysis and the spectroscopic VVDS data.
