On the modified skew-normal-Cauchy distribution: properties, inference and applications

In this paper, we study further properties of the modified skew-normal-Cauchy (MSNC) distribution. MSNC distribution corresponds to a reformulation of skew-normal-Cauchy distribution that allows to obtain a nonsingular Fisher Information Matrix at skewness parameter equal zero. We suggest a hierarchical representation which allows alternative derivations for moments generating function, moments, and skewness and kurtosis coefficients. As an application, we develop hypothesis testing for normality considering the Kullback–Leibler divergence between MSNC distribution and the normal one. Finally, we apply this result to condition factor time series of shortfin mako sharks off northern Chile.