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<p>In this paper, we propose a flexible scale mixtures of the skewed generalized normal (FSMSGN) distributions, which encompasses several well-known asymmetric distributions as special cases. Within this general framework, we derive key distributional properties and introduce an efficient ECME-PLA algorithm that combines the Profile Likelihood Approach (PLA) with the classical Expectation/Conditional Maximization Either (ECME) algorithm to obtain maximum likelihood estimates (MLEs) of the model parameters, overcoming the convergence challenges faced by traditional methods. We further extend the method to linear regression models with FSMSGN-distributed errors and derive the corresponding updating equations for the regression coefficients. The asymptotic properties of the proposed estimators are also investigated. A comprehensive simulation study demonstrates the strong performance of the proposed approach, particularly in modeling skewed, heavy-tailed, and peaked data. The practical effectiveness of the method is illustrated through applications to three real-world datasets.</p>

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Flexible scale mixtures of skewed generalized normal distributions: properties and inference

  • 期刊论文

  • 发表日期：

    2026年1月13日

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  • Aidi Liu,
  • Weihu Cheng,
  • Minghui Yao

摘要

In this paper, we propose a flexible scale mixtures of the skewed generalized normal (FSMSGN) distributions, which encompasses several well-known asymmetric distributions as special cases. Within this general framework, we derive key distributional properties and introduce an efficient ECME-PLA algorithm that combines the Profile Likelihood Approach (PLA) with the classical Expectation/Conditional Maximization Either (ECME) algorithm to obtain maximum likelihood estimates (MLEs) of the model parameters, overcoming the convergence challenges faced by traditional methods. We further extend the method to linear regression models with FSMSGN-distributed errors and derive the corresponding updating equations for the regression coefficients. The asymptotic properties of the proposed estimators are also investigated. A comprehensive simulation study demonstrates the strong performance of the proposed approach, particularly in modeling skewed, heavy-tailed, and peaked data. The practical effectiveness of the method is illustrated through applications to three real-world datasets.