A novel finite mixture model based on the generalized scale mixtures of asymmetric generalized normal distributions: properties, estimation methodology and applications

In this paper, we introduce a family of distributions known as generalized scale mixtures of asymmetric generalized normal distributions (GSMAGN), characterized by remarkable flexibility in shape. We propose a novel finite mixture model based on this distribution family, offering an effective tool for modeling intricate data featuring skewness, heavy tails, and multi-modality. To facilitate parameter estimation for this model, we devise an ECM-PLA ensemble algorithm that combines the Profile Likelihood Approach (PLA) with the classical Expectation Conditional Maximization (ECM) algorithm. By incorporating analytical expressions in the E-step and manageable computations in the M-step, this approach significantly enhances computational speed and overall efficiency. Furthermore, we persent the closed-form expressions for the observed information matrix, which serves as an approximation for the asymptotic covariance matrix of the maximum likelihood estimates. Additionally, we expound upon the corresponding consistency characteristics inherent to this particular mixture model. The applicability of the proposed model is elucidated through several simulation studies and practical datasets.