The random nature of light emitters requires that the theory to study polarization must adopt a statistical approach. Although the Stokes parameters are proposed in this sense, these are implemented as temporal averages, appealing to an ergodic hypothesis, without discussing which probability distributions are treated. Therefore, here the polarization dynamics on the Poincaré sphere of random light sources, whose phases and amplitudes of the electric fields are statistically independent, is described through the von Mises–Fisher distribution. This allows us to relate the degree of polarization and the normalized Stokes parameters with the concentration parameter and the mean direction of the von Mises–Fisher distribution. Also, it is found that their marginal distributions have the same statistical behavior as the Eliyahu–Brosseau distribution.
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