Construction and parameter estimation of wrapped normal models

Abstract

If a known distribution on a real line is given, it can be wrapped on the circumference of a unit circle. This research entails the study of a univariate skew-normal distribution where the skew-normal distribution is generalised for the case of bimodality. Both the skew-normal and exible generalised skew-normal distributions are wrapped onto a unit circle, consequently referred to as a wrapped skew-normal and a wrapped exible generalised skew-normal distribution respectively. For each of these distributions a simulation study is conducted, where the performance of maximum likelihood estimation is evaluated. Skew scale mixtures of normal distributions with the wrapped version of these distributions are proposed and graphical representations are provided. These distributions are also compared in an application to wind direction data.