Measurements of linear dichroism and of polarized fluorescence of 2-fluoropyrene (2-F-1) in stretched linear low-density polyethylene (LLDPE) at 77K have been used to evaluate the two independent second moments, 〈cos2 z〉 and 〈cos2 y〉, as well as the three independent fourth moments, 〈cos4 z〉, 〈cos4 y〉, and 〈cos4 x〉, of the orientation distribution function. The results are used to discuss two previously proposed detailed models for the mechanism of the orientation of aromatics in stretched polyethylene. For pyrene (1) and 2-methylpyrene (2-Me-1), four of the five moments were obtained. In these two molecules the direction of the Lb transition moment does not coincide with the molecular short in-plane y axis, but shows a distribution of orientations within the molecular framework, revealed by a site-selection experiment. On the average, it is inclined approximately 40° and 20° away from the y axis in the two compounds, respectively. This behavior is ascribed to a symmetry-lowering perturbation by the environment, related to the Ham effect.