  A statistical framework is presented for the study of the orthogonally
polarized modes of radio pulsar emission via the covariances between the Stokes
parameters. To accommodate the typically heavy-tailed distributions of
single-pulse radio flux density, the fourth-order joint cumulants of the
electric field are used to describe the superposition of modes with arbitrary
probability distributions. The framework is used to consider the distinction
between superposed and disjoint modes with particular attention to the effects
of integration over finite samples. If the interval over which the polarization
state is estimated is longer than the timescale for switching between two or
more disjoint modes of emission, then the modes are unresolved by the
instrument. The resulting composite sample mean exhibits properties that have
been attributed to mode superposition, such as depolarization. Because the
distinction between disjoint modes and a composite sample of unresolved
disjoint modes depends on the temporal resolution of the observing
instrumentation, the arguments in favour of superposed modes of pulsar emission
are revisited and observational evidence for disjoint modes is described. In
principle, the four-dimensional covariance matrix that describes the
distribution of sample mean Stokes parameters can be used to distinguish
between disjoint modes, superposed modes, and a composite sample of unresolved
disjoint modes. More comprehensive and conclusive interpretation of the
covariance matrix requires more detailed consideration of various relevant
phenomena, including temporally correlated subpulse modulation (e.g. jitter),
statistical dependence between modes (e.g. covariant intensities and partial
coherence), and multipath propagation effects (e.g. scintillation and
scattering). Unpublished supplementary material is appended after the
bibliography.
