Directional Statistics for Polarization Observations of Individual
  Pulses from Radio Pulsars
  Radio polarimetry is a three-dimensional statistical problem. The
three-dimensional aspect of the problem arises from the Stokes parameters Q, U,
and V, which completely describe the polarization of electromagnetic radiation
and conceptually define the orientation of a polarization vector in the
Poincar'e sphere. The statistical aspect of the problem arises from the random
fluctuations in the source-intrinsic polarization and the instrumental noise. A
simple model for the polarization of pulsar radio emission has been used to
derive the three-dimensional statistics of radio polarimetry. The model is
based upon the proposition that the observed polarization is due to the
incoherent superposition of two, highly polarized, orthogonal modes. The
directional statistics derived from the model follow the Bingham-Mardia and
Fisher family of distributions. The model assumptions are supported by the
qualitative agreement between the statistics derived from it and those measured
with polarization observations of the individual pulses from pulsars. The
orthogonal modes are thought to be the natural modes of radio wave propagation
in the pulsar magnetosphere. The intensities of the modes become statistically
independent when generalized Faraday rotation (GFR) in the magnetosphere causes
the difference in their phases to be large. A stochastic version of GFR occurs
when fluctuations in the phase difference are also large, and may be
responsible for the more complicated polarization patterns observed in pulsar
radio emission.
