Title: A generalised normal distribution with interpretable parameters for location, body-shape, skewness, and tail-weight
Authors: Andriette Bekker - University of Pretoria (South Africa)
Mohammad Arashi - Ferdowsi University of Mashhad (Iran)
Matthias Wagener - University of Pretoria (South Africa) [presenting]
Abstract: The multivariate normal distribution is a foundational model in statistics. There are many generalised forms for modelling non-normal and irregular data. However, very few of these generalisations have shape parameters with clear roles that determine, for instance, skewness and tail shape. Here, we add a skewness parameter for the body-tail generalised normal distribution, which yields the flexible and interpretable normal distribution FIN with parameters for location, scale, body-shape, skewness, and tail weight. Basic statistical properties of the FIN are provided, such as the density function, cumulative density function, moments, and likelihood equations. The FIN density is extended to a multivariate setting using a student t-copula, yielding the multivariate FIN distribution MFIN. The MFIN is applied to stock returns data where it is compared to the t-copula multivariate sinh-arcsinh, skew-t, and hyperbolic distribution.