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.
