Context : Knowing the exact shape of the ultraviolet ( UV ) luminosity function ( LF ) of high-redshift galaxies is important to understand the star formation history of the early Universe .
However , the uncertainties , especially at the faint and bright ends of the LFs , remain significant .

Aims : In this paper , we study the UV LF of redshift z = 2.5 - 4.5 galaxies in 2.38 deg ^ { 2 } of ALHAMBRA data with I \leq 24 .
Thanks to the large area covered by ALHAMBRA , we particularly constrain the bright end of the LF .
We also calculate the cosmic variance and the corresponding bias values for our sample and derive their host dark matter halo masses .

Methods : We have used 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 LF in two dimensions ( z,M _ { UV } ) .

Results : We find an excess of bright \sim M ^ { \ast } _ { UV } galaxies as compared to the studies based on broad-band photometric data .
However , our results agree well with the LF of the magnitude-selected spectroscopic VVDS data .
We measure high bias values , b \sim 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 LF 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 .