Geometrical optics and the statistical analysis of refractive error

Relationships among statistical quantities used in the analysis of refractive error are derived from geometrical optics principles. The accuracy of these results are verified using the data of Sorsby et al. As an application of these results, it is shown that there is difficulty in accounting for leptokurtosis of refractive error in terms of correlation among the optical parameters of the eye. Also, it is shown that the distribution of the optical parameters of the eye cannot be a joint-normal distribution.