We have compiled a sample of 45 Type Ia supernovae (SNe Ia) discovered by t
he Lick Observatory Supernova Search (LOSS) and the Beijing Astronomical Ob
servatory Supernova Survey (BAOSS), and determined the rate of spectroscopi
cally peculiar SNe Ia (i.e., SN 1986G-like, SN 1991bg-like, and SN 1991T-li
ke objects) and the luminosity function of SNe Ia. Because of the nature of
the two surveys (distance-limited with small baselines and deep limiting m
agnitudes), nearly all SNe Ia have been discovered in the sample galaxies o
f LOSS and BAOSS; thus, the observed peculiarity rate and luminosity functi
on of SNe Ia are intrinsic. We find that 36% +/- 9% of nearby SNe Ia are pe
culiar; specifically, the luminosity function of SNe Ia consists of 20% SN
1991T-like, 64% normal, and 16% SN 1991bg-like objects. We have compared ou
r results to those found by earlier studies, and to those found at high red
shift. The apparent dearth of SN 1991T-like objects at high redshift may be
due to extinction, and especially to the difficulty of recognizing them fr
om spectra obtained past maximum brightness or from spectra with low signal
-to-noise ratios. Implications of the high peculiarity rate for the progeni
tor systems of SNe Ia are also briefly discussed.