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The luminosity function (LF) for stars is here fitted by a Schechter functionand by a Gamma probability density function. The dependence of the number ofstars on the distance, both in the low and high luminosity regions, requiresthe inclusion of a lower and upper boundary in the Schechter and Gamma LFs.Three astrophysical applications for stars are provided: deduction of theparameters at low distances, behavior of the average absolute magnitude withdistance, and the location of the photometric maximum as a function of theselected flux. The use of the truncated LFs allows to model the Malmquist bias.

Standard and Truncated Luminosity Functions for stars in the Gaia Era