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We propose a novel estimator of the polarization amplitude from a singlemeasurement of its normally distributed $(Q,U)$ Stokes components. Based on theproperties of the Rice distribution and dubbed 'MAS' (Modified ASymptotic), itmeets several desirable criteria:(i) its values lie in the whole positiveregion; (ii) its distribution is continuous; (iii) it transforms smoothly withthe signal-to-noise ratio (SNR) from a Rayleigh-like shape to a Gaussian one;(iv) it is unbiased and reaches its components' variance as soon as the SNRexceeds 2; (v) it is analytic and can therefore be used on large data-sets. Wealso revisit the construction of its associated confidence intervals and showhow the Feldman-Cousins prescription efficiently solves the issue of classicalintervals lying entirely in the unphysical negative domain. Such intervals canbe used to identify statistically significant polarized regions and converselybuild masks for polarization data. We then consider the case of a general$[Q,U]$ covariance matrix and perform a generalization of the estimator thatpreserves its asymptotic properties. We show that its bias does not depend onthe true polarization angle, and provide an analytic estimate of its variance.The estimator value, together with its variance, provide a powerfulpoint-estimate of the true polarization amplitude that follows an unbiasedGaussian distribution for a SNR as low as 2. These results can be applied tothe much more general case of transforming any normally distributed randomvariable from Cartesian to polar coordinates.

A novel estimator of the polarization amplitude from normally distributed Stokes parameters