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.