We investigate the differential size-frequency
distribution (SFD) of Jupiter Family comets (JFCs) in order to determine whether
they are primordial accreted objects or collisional fragments as suggested by
current models of the evolution of Trans-Neptunian Objects (TNOs). We develop a
list of effective radii and their uncertainties for 161 active JFCs from
published sources and compute the observed differential size-frequency
distribution using a Probability Index technique. The radii range from 0.2 to
15.4 km and average 1.9 km. The peak of the distribution is near 1.0 km. This is
then corrected for the effects of observational selection using a model
published earlier by Meech *et al.* (Icarus
170, 463-491, 2004). We estimate
that the total number of active* *JFCs
between 0.2 and 15.4 km is approximately
2300
indicating that our current sample of the of active JFC population is far from
complete. The active JFC size-frequency distribution, over the range from 0.6 to
10 km where it is best defined, is found to be closer to an exponential
distribution in character than a power-law. We then develop a statistical model,
based on the assumption of a steady state, for converting the distribution of
active JFCs to the SFD of the source population among the TNOs. The model
includes the effects of devolatization (that produces a large sub-class of
defunct nuclei) and surficial mass-loss. Comparison with available TNO
observations shows that to simultaneously attain continuity with the data on
objects in the hot TNO population (Fuentes *
et al.* (Astrophys.J 722,1290-1304; 2010), satisfy constraints on the number
of TNOs set by the occultation detections of Schlichting
*et al.* (Ap.J. 761:150; 2012), and to
remain within upper limits set by the Taiwanese-American Occultation Survey
(TAOS; Zhang *et al,* Astron. J. 146, Id
14, 10pp) the total JFC population must contain a large fraction of small
defunct nuclei. The effective power-law index of the inferred TNO differential
SFD between 1 and 10 km is -4.5 +/- 0.5 indicating a population in this range
that is not in fully relaxed collisional equilibrium. We conclude that the
cometary nuclei so far visited by spacecraft and many JFCs are primordial
accreted objects relatively unaffected by collisional evolution. We find a
turndown in the slope of the predicted TNO cumulative distribution near 1 km
radius rather than near 10 km that is seen in many TNO evolutionary
calculations. This may or may not represent the onset of a collisional cascade.