  A sample of close major-merger pairs (projected separation ${\rm 5 \leq r
\leq 20 h^{-1}}$ kpc, ${\rm K_s}$ band magnitude difference $\delta {\rm K_s}
\leq 1$ mag) is selected from the matched 2MASS-2dFGRS catalog of Cole et al.
(2001). The pair primaries are brighter than ${\rm K_s} = 12.5$ mag. After
corrections for various biases, the comparison between counts in the paired
galaxy sample and counts in the parent sample shows that for the local `M*
galaxies' sampled by flux limited surveys, the fraction of galaxies in the
close major-merger pairs is 1.70$\pm 0.32%$. Using 38 paired galaxies in the
sample, a ${\rm K_s}$ band luminosity function (LF) is calculated. This is the
first unbiased LF for a sample of objectively defined interacting/merging
galaxies in the local universe, while all previously determined LFs of paired
galaxies are biased by mistreating paired galaxies as singles. A stellar mass
function (MF) is translated from the LF. Compared to the LF/MF of 2MASS
galaxies, a differential pair fraction function is derived. The results suggest
a trend in the sense that less massive galaxies may have lower chance to be
involved in close major-merger pairs than more massive galaxies. The algorithm
presented in this paper can be easily applied to much larger samples of 2MASS
galaxies with redshifts in near future.
