Statistical Properties of the Estimated Degree of Polarization

We derive important and useful new statistical properties of the estimated degree of polarization in the two-dimensional case. We find its distribution function and show how it may be used to construct confidence intervals. We also find an expression for any moment of the distribution, and derive an exact unbiasing formula for the estimator of the squared coefficient. Further we discuss a test for partial polarization. Our statistical analyses enable identification of elliptical polarization for an ultra low frequency wave in the solar magnetic field.