Skew–Normal Mean–Variance Mixture of Birnbaum–Saunders Distribution and Its Associated Inference and Application

This paper presents a skew-normal mean-variance mixture based on Birnbaum-Saunders (SNMVBS) distribution and discusses some of its key properties. The SNMVBS distribution can be thought as a flexible extension of the normal mean-variance mixture based on Birnbaum-Saunders (NMVBS) distribution as it possesses one additional shape parameter for providing more flexibility with skewness and kurtosis. Next, we develop a computationally feasible ECM algorithm for the maximum likelihood estimation of the model parameters. Asymptotic standard errors of the ML estimates are obtained through an approximation of the observed information matrix. Finally, the usefulness of the proposed model and its fitting method are illustrated through a Monte-Carlo simulation as well as three real-life datasets.