Electron Backscatter Diffraction (EBSD) is a technique used in materials science to study the microtexture of metals, producing data which measure orientations of crystals in a specimen. We examine the precision of such data based on a useful class of distributions on orientations in 3 dimensions (as represented by 3 × 3 orthogonal matrices with positive determinant). While such modeling has received attention in the statistical literature, the approach taken has typically been from general

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... cial manifold" considerations and the resulting methodology may not be easily accessible to non-specialists. We take a more direct modeling approach, beginning from a simple intuitively appealing mechanism for generating random orientations specifically in 3-space. The resulting class of distributions has many desirable properties, including directly interpretable parameters and relatively simple theory. We investigate the basic properties of the entire class and one-sample quasi-likelihood-based 1 inference for one member of the model class, producing new statistical methodology that proves practically useful in the analysis of EBSD data.