  I have undertaken a comprehensive statistical investigation of the ultracool
dwarf companion distribution (spectral type M6 and later). Utilizing a Bayesian
algorithm, I tested models of the companion distribution against data from an
extensive set of space and ground-based imaging observations of nearby
ultracool dwarfs. My main conclusions are fivefold: 1) Confirm that the
concentration of high mass ratio ultracool binary systems is a fundamental
feature of the companion distribution, not an observational or selection bias;
2) Determine that the wide (>~20 AU) binary frequency can be no more the 1-2%;
3) Show that the decreasing binary frequency with later spectral types is a
real trend; 4) Demonstrate that a large population of currently undetected low
mass ratio systems are not consistent with the current data; 5) Find that the
population of spectroscopic binaries must be be at least 30% that of currently
known ultracool binaries. The best fit value for the overall M6 and later
binary frequency is ~20%-22%, of which only ~6% consists of currently
undetected companions with separations less than 1 AU. If this is correct, then
the upper limit of the ultracool binary population discovered to date is ~75%.
I find that the numerical simulation results of the ejection formation method
are inconsistent with the outcome of this analysis. However, dynamics do seem
to play an important role as simulations of small-N clusters and triple system
decays produce results similar to those of this work. The observational efforts
required to improve these constraints are shown to be primarily large
spectroscopic binary surveys and improved high-resolution imaging techniques.
