A novel finite mixture model based on generalized scale mixtures of generalized normal distributions with application to stock dataset

This paper introduces a novel family of distributions known as generalized scale mixtures of generalized normal distributions (GSMGN). These distributions incorporate two additional shape parameters that serve to regulate the shape and tails of the distribution. A finite mixture model based on this family is presented to address clustering heterogeneous data in the presence of leptokurtic and heavy-tailed outcomes. The estimation of the parameters of this model are obtained by developing an ECM-PLA ensemble algorithm which combine the profile likelihood approach (PLA) and the classical Expectation Conditional Maximization (ECM) algorithm, and the observed information matrix is obtained. The applicability of this new family and the numerical performance of the proposed methodology is discussed through simulated and real data examples.