  We present the optical and near-infrared luminosity and mass functions of the
local star-forming galaxies in the Universidad Complutense de Madrid Survey. A
bivariate method which explicitly deals with the Halpha selection of the survey
is used when estimating these functions. Total stellar masses have been
calculated on a galaxy-by-galaxy basis taking into account differences in star
formation histories. The main difference between the luminosity distributions
of the UCM sample and the luminosity functions of the local galaxy population
is a lower normalization (phi^*), indicating a lower global volume density of
UCM galaxies. The typical near-infrared luminosity (L^*) of local star-forming
galaxies is fainter than that of normal galaxies. This is a direct consequence
of the lower stellar masses of our objects. However, at optical wavelengths (B
and r) the luminosity enhancement arising from the young stars leads to M^*
values that are similar to those of normal galaxies. The fraction of the total
optical and near infrared luminosity density in the local Universe associated
with star-forming galaxies is 10-20%. Fitting the total stellar mass function
using a Schechter parametrization we obtain alpha=-1.15+/-0.15,
log({M}^*)=10.82+/-0.17 Msun and log(phi^*)=-3.04+/-0.20 Mpc^{-3}. This gives
an integrated total stellar mass density of 10^{7.83+/-0.07} Msun Mpc^{-3} in
local star-forming galaxies (H_0=70 km s^{-1} Mpc^{-1}, Omega_M=0.3,
Lambda=0.7). The volume-averaged burst strength of the UCM galaxies is
b=0.04+/-0.01, defined as the ratio of the mass density of stars formed in
recent bursts (age<10 Myr) to the total stellar mass density in UCM galaxies.
Finally, we derive that, in the local Universe, (13+/-3)% of the total baryon
mass density in the form of stars is associated with star-forming galaxies.
