Title: New contributions to Mobius transformation induced distributions on the disc
Authors: Priyanka Nagar - University of Pretoria (South Africa) [presenting]
Andriette Bekker - University of Pretoria (South Africa)
Mohammad Arashi - Shahrood University of Technology (Iran)
Abstract: There is a need for developing flexible distributions on the hyper-disc, which has support of the interior of the hyper-sphere, as it allows for modelling the combination of angular and linear observations. A new family of distributions is proposed which has support on the unit disc in two dimensions that includes the bivariate spherically symmetric beta distribution. By applying a conformal mapping to this distribution the new Mobius distribution class emanates. Modality, symmetry, marginal distributions and maximum likelihood estimation are considered. The flexible behaviour of the proposed models on the hyper-disc will be graphically demonstrated and applied to model fitting.