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We have developed a Monte Carlo method to compute the luminosity function ofgalaxies, based on photometric redshifts, which takes into account thenon-gaussianity of the probability functions, and the presence of degeneratesolutions in redshift. In this paper we describe the method and the mock testsperformed to check its reliability. The NIR luminosity functions and theredshift distributions are determined for near infrared subsamples on the HDF-Nand HDF-S. The results on the evolution of the NIR LF, the stellar massfunction, and the luminosity density, are presented and discussed in view ofthe implications for the galaxy formation models. The main results are the lackof substantial evolution of the bright end of the NIR LF and the absence ofdecline of the luminosity density up to a redshift z ~ 2, implying that most ofthe stellar population in massive galaxies was already in place at suchredshift.Comment: 23 pages, 19 figures. Accepted for publication in A&A. No change

Luminosity functions beyond the spectroscopic limit