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<p>The proliferation of complex data across various domains has led to an increasing prevalence of skewed and heavy-tailed distributions, where traditional symmetric distributions become inadequate. While existing approaches like the skew-normal distribution have addressed this challenge, they remain constrained by limited ranges of skewness and kurtosis, particularly in handling extreme cases. In this study, we introduce the Skewed Generalized Normal (SGN) distribution, a novel and highly flexible distribution class capable of capturing an extensive range of skewness and kurtosis while maintaining mathematical tractability. We establish its theoretical foundation through comprehensive analysis of its properties and develop two robust parameter estimation methods: a classical Expectation-Maximization (EM) algorithm and an innovative deep learning-based approach called EstiFormer. The latter represents a significant advancement in parameter estimation, offering a pre-trained, adaptable model for rapid and precise estimation across diverse data scenarios. Through extensive simulation studies with varying sample sizes, we demonstrate that both estimation methods achieve high accuracy, with the SGN distribution significantly outperforming existing alternatives in fitting highly skewed and kurtotic data. Applications to real-world datasets further validate the SGN distribution’s superior flexibility and practical utility.</p>

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Properties and Estimation of a Novel Skewed Generalized Normal Distribution

  • 期刊论文

  • 发表日期：

    2025年12月16日

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  • Xue Wang,
  • Weihu Cheng,
  • Minghan Wang,
  • Xu Zhao

摘要

The proliferation of complex data across various domains has led to an increasing prevalence of skewed and heavy-tailed distributions, where traditional symmetric distributions become inadequate. While existing approaches like the skew-normal distribution have addressed this challenge, they remain constrained by limited ranges of skewness and kurtosis, particularly in handling extreme cases. In this study, we introduce the Skewed Generalized Normal (SGN) distribution, a novel and highly flexible distribution class capable of capturing an extensive range of skewness and kurtosis while maintaining mathematical tractability. We establish its theoretical foundation through comprehensive analysis of its properties and develop two robust parameter estimation methods: a classical Expectation-Maximization (EM) algorithm and an innovative deep learning-based approach called EstiFormer. The latter represents a significant advancement in parameter estimation, offering a pre-trained, adaptable model for rapid and precise estimation across diverse data scenarios. Through extensive simulation studies with varying sample sizes, we demonstrate that both estimation methods achieve high accuracy, with the SGN distribution significantly outperforming existing alternatives in fitting highly skewed and kurtotic data. Applications to real-world datasets further validate the SGN distribution’s superior flexibility and practical utility.