  Because of their proximity within the transneptunian region, the plutinos
(objects in the 3:2 mean-motion resonance with Neptune) are numerous in
flux-limited catalogs, and well-studied theoretically. We perform detailed
modelling of the on-sky detection biases for plutinos, with special attention
to those that are simultaneously in the Kozai resonance. In addition to the
normal 3:2 resonant argument libration, Kozai plutinos also show periodic
oscillations in eccentricity and inclination, coupled to the argument of
perihelion (omega) oscillation. Due to the mean-motion resonance, plutinos
avoid coming to pericenter near Neptune's current position in the ecliptic
plane. Because Kozai plutinos are restricted to certain values of omega,
perihelion always occurs out of the ecliptic plane, biasing ecliptic surveys
against finding these objects. The observed Kozai plutino fraction (fkoz) has
been measured by several surveys, finding values between 8% and 25%, while the
true fkoz has been predicted to be between 10% and 30% by different giant
planet migration simulations. We show that the observed fkoz varies widely
depending on the ecliptic latitude and longitude of the survey, so debiasing to
find the true ratio is complex. Even a survey that covers most or all of the
sky will detect an apparent Kozai fraction that is different from the true
fkoz. We present a map of the on-sky plutino Kozai fraction that would be
detected by all-sky flux-limited surveys. This will be especially important for
the Panoramic Survey Telescope & Rapid Response System (Pan-STARRS) and Large
Synoptic Survey Telescope (LSST) projects, which may detect large numbers of
plutinos as they sweep the sky. The Kozai fraction and the distribution of the
orbital elements of Kozai plutinos may be a diagnostic of giant planet
migration; future migration simulations should provide details on their
resonant Kozai populations.
