Abstract: A Wishart model is proposed for random distance matrices in which the components are correlated gamma random variables, all having the same degrees of freedom. The marginal likelihood is obtained in closed form. Its use is illustrated by multidimensional scaling, by rooted tree models for response covariances in social survey work, and unrooted trees for ancestral relationships in genetic applications.
Key words and phrases: Generalized Gaussian distribution, maximum-likelihood tree, multi-dimensional scaling, REML, residual maximum likelihood, tree-structured covariance matrix, unrooted tree, Wishart distribution.