Abstract

: Compositional datasets arise naturally in a multiplicity of fields such as archaeology, geology,
and biological sciences. In this study, the square-root transformation on Dirichlet-type random
variables is used in constructing a distribution defined on the positive orthant of the hypersphere.
The transformation on these random variables results in a novel model that is an offering to the family
of spherical-Dirichlet distributions. The maximum likelihood estimation is used for the parameter
estimation of the proposed model, where applications in the biological and archaeological sciences is
presented, to illustrate the flexibility of the proposed model.