Skew-normal distribution, Generalized skew-normal distribution, Two-piece skew-normal distribution, Generalized two-piece skew-normal distribution, Generalized skew two-piece skew-normal distribution, Unimodality and bimodality, Orthant probability,

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Abstract. This paper presents a new finite mixture model using the normal meanvariance mixture of Birnbaum-Saunders distribution. The proposed model is multimodal with wider ranges of skewness and kurtosis. Moreover, it is useful for modeling highly asymmetric data in various theoretical and applied statistical problems. The maximum likelihood estimates of the parameters of the model are computed iteratively by feasible EM algorithm. To illustrate the finite sample properties and performance of the estimators, we conduct a simulation study and illustrate the usefulness of the new model by analyzing a real dataset.