The object of this project is the study of multivariate ratios or proportions. Studies of random proportions and ratios, including those that follow a multivariate lognormal distribution as well as those following the distribution of a mixture of Dirichlet distributions, were continued. In the past year, the major emphasis was on obtaining closed form solutions for the eigenvalues and eigenvectors of certain patterned matrices that arise frequently with biological data. The patterns are those of """"""""persymmetric"""""""" (includes Toeplitz) matrices, as well as a pattern that reflects a single """"""""unique or dominant"""""""" variable related to any number of variables equicorrelated among themselves. In addition, a paper with M. V. Ratnaparkhi on normalizing transformations of ratios and proportions was completed.
