  Inspired by recent use of polarimetry to study the Cosmic Microwave
Background and extragalatic supernovae, a foray into the statistical properties
of Stokes parameters expressed in spherical coordinates is began, allowing
circular polarization and linear polarization to be treated in a unified
manner. The use of spherical coordinates is quite necessary as it permits a
Stokes polarization state to be expressed in terms of the customary
polarization angles and degree of polarization usually needed for human
interpretation. As shall be demonstrated, circular and linear polarization are
not statistically independent quantities but intertwined in a way that is
especially important, for instance, at low signal-to-noise. New distributions,
classical estimators, and marginalizations are presented for this
"three-dimensional" polarization problem including a generalization of the Rice
distribution. The paper concludes with discussion regarding the potential
pitfalls of a lower dimensional analysis.
