  Small solar system bodies have widely dispersed orbital poles, posing
challenges to dynamical models of solar system origin and evolution. To
characterize the orbit pole distribution of dynamical groups of small bodies it
helps to have a functional form for a model of the distribution function.
Previous studies have used the small-inclination approximation and adopted
variations of the normal distribution to model orbital inclination dispersions.
Because the orbital pole is a directional variable, its distribution can be
more appropriately modeled with directional statistics. We describe the von
Mises-Fisher (vMF) distribution on the surface of the unit sphere for
application to small bodies' orbital poles. We apply it to the orbit pole
distribution of the observed Plutinos. We find a mean pole located at
inclination of 3.57 degrees and a longitude of ascending node of 124.38 degrees
(in the J2000 reference frame), with a 99.7 per cent confidence cone of
half-angle 1.68 degrees. We also estimate a debiased mean pole located 4.6
degrees away, at an inclination of 2.26 degrees and a longitude of ascending
node of 292.69 degrees, of similar-size confidence cone. The vMF concentration
parameter of Plutino inclinations (relative to either mean pole estimate) is
31.6. This resembles a Rayleigh distribution function with a width parameter of
10.2 degrees. Unlike previous models, the vMF model naturally accommodates all
physical inclinations (and no others), whereas Rayleigh or Gaussian models must
be truncated to the physical inclination range 0-180 degrees. Further work is
needed to produce a theory for the mean pole of the Plutinos against which to
compare the observational results.
