  The increase in the number of Type Ia supernovae (SNe\,Ia) has demonstrated
that the population shows larger diversity than has been assumed in the past.
The reasons (e.g. parent population, explosion mechanism) for this diversity
remain largely unknown. We have investigated a sample of SNe\,Ia near-infrared
light curves and have correlated the phase of the second maximum with the
bolometric peak luminosity. The peak bolometric luminosity is related to the
time of the second maximum (relative to the {\it B} light curve maximum) as
follows : $L_{max}(10^{43} erg s^{-1}) = (0.039 \pm 0.004) \times t_2(J)(days)
+ (0.013 \pm 0.106)$.
  $^{56}$Ni masses can be derived from the peak luminosity based on Arnett's
rule, which states that the luminosity at maximum is equal to instantaneous
energy generated by the nickel decay. We check this assumption against recent
radiative-transfer calculations of Chandrasekhar-mass delayed detonation models
and find this assumption is valid to within 10\% in recent radiative-transfer
calculations of Chandrasekhar-mass delayed detonation models.
  The $L_{max}$ vs. $t_2$ relation is applied to a sample of 40 additional
SNe\,Ia with significant reddening ($E(B-V) >$ 0.1 mag) and a reddening-free
bolometric luminosity function of SNe~Ia is established. The method is tested
with the $^{56}$Ni mass measurement from the direct observation of
$\gamma-$rays in the heavily absorbed SN 2014J and found to be fully
consistent.
  Super-Chandrasekhar-mass explosions, in particular SN\,2007if, do not follow
the relations between peak luminosity and second IR maximum. This may point to
an additional energy source contributing at maximum light.
  The luminosity function of SNe\,Ia is constructed and is shown to be
asymmetric with a tail of low-luminosity objects and a rather sharp
high-luminosity cutoff, although it might be influenced by selection effects.
