  The Deep Ecliptic Survey (DES) discovered hundreds of Kuiper Belt objects
from 1998-2005. Follow-up observations yielded 304 objects with good dynamical
classifications (Classical, Scattered, Centaur, or 16 mean-motion resonances
with Neptune). The DES search fields are well documented, enabling us to
calculate the probability of detecting objects with particular orbital
parameters and absolute magnitudes at a randomized point in each orbit.
Grouping objects together by dynamical class leads, we estimate the orbital
element distributions (a, e, i) for the largest three classes (Classical, 3:2,
and Scattered) using maximum likelihood. Using H-magnitude as a proxy for the
object size, we fit a power law to the number of objects for 8 classes with at
least 5 detected members (246 objects). The best Classical slope is
alpha=1.02+/-0.01 (observed from 5<=H<=7.2). Six dynamical classes (Scattered
plus 5 resonances) are consistent in slope with the Classicals, though the
absolute number of objects is scaled. The exception to the power law relation
are the Centaurs (non-resonant with perihelia closer than Neptune, and thus
detectable at smaller sizes), with alpha=0.42+/-0.02 (7.5<H<11). This is
consistent with a knee in the H-distribution around H=7.2 as reported elsewhere
(Bernstein et al. 2004, Fraser et al. 2014). Based on the Classical-derived
magnitude distribution, the total number of objects (H<=7) in each class are:
Classical (2100+/-300 objects), Scattered (2800+/-400), 3:2 (570+/-80), 2:1
(400+/-50), 5:2 (270+/-40), 7:4 (69+/-9), 5:3 (60+/-8). The independent
estimate for the number of Centaurs in the same H range is 13+/-5. If instead
all objects are divided by inclination into "Hot" and "Cold" populations,
following Fraser et al. (2014), we find that alphaHot=0.90+/-0.02, while
alphaCold=1.32+/-0.02, in good agreement with that work.
