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The quaternion Bingham distribution has been used to model preferredcrystallographic orientation, or crystallographic texture, in polycrystallinematerials in the materials science and geological communities. A primarydifficulty in applying the Bingham distribution has been the lack of anefficient method for fitting the distribution parameters with respect to thematerials underlying crystallographic symmetry or any statistical samplesymmetry due to processing. In this paper we present a symmetrizeddistribution, based on the quaternion Bingham, which can account for anygeneral combination of crystallographic or sample symmetries. We also introducea numerical scheme for estimating the parameters of the symmetrizeddistribution based on the well known expectation maximization algorithm.

Symmetrized Bingham Distribution for Representing Texture: Parameter estimation with respect to crystal and sample symmetries