Point and interval estimation of the true unbiased degree of linear polarization in the presence of low signal-to-noise ratios

Four estimators which attempt to correct for biasing in the degree of linear polarization are discussed for the specific case when the errors on an observation of the normalized Stokes parameters q and u are known and assumed equal to sigma. Expressions are derived for the different estimators and their respective distributions and bias which all differ significantly at low polarizations or low SNR levels are investigated. A method for establishing confidence intervals for the degree of polarization is presented in a form useful to the observer. Some applications of these results to different astrophysical situations are discussed.