标题： 约束混合广义正态分布 显示英文标题

标题： Constrained mixtures of generalized normal distributions

摘要： 本文介绍了一类具有约束条件的多元广义正态分布混合模型（CMGND），其中位置、尺度和形状参数可以在混合成分的任意子集上被约束为相等。采用带牛顿-拉弗森更新的期望条件最大化（ECM）算法，在约束条件下估计模型参数。仿真研究表明，施加正确的约束比无约束混合模型能更准确地估计参数，尤其是在组分显著重叠时。约束模型在捕捉边缘分布的关键特性（如峰度）方面也表现出竞争力。在每日股票指数收益率的真实数据集上，基于BIC准则，CMGND模型优于正态分布和Student's t分布的约束混合模型，突显了其在建模非正态特征方面的灵活性。所提出的约束方法提高了可解释性，并能在不牺牲复杂数据分布灵活性的前提下提高参数效率。 显示英文摘要

摘要： This work introduces a family of univariate constrained mixtures of generalized normal distributions (CMGND) where the location, scale, and shape parameters can be constrained to be equal across any subset of mixture components. An expectation conditional maximisation (ECM) algorithm with Newton-Raphson updates is used to estimate the model parameters under the constraints. Simulation studies demonstrate that imposing correct constraints leads to more accurate parameter estimation compared to unconstrained mixtures, especially when components substantially overlap. Constrained models also exhibit competitive performance in capturing key characteristics of the marginal distribution, such as kurtosis. On a real dataset of daily stock index returns, CMGND models outperform constrained mixtures of normals and Student's t distributions based on the BIC criterion, highlighting their flexibility in modelling nonnormal features. The proposed constrained approach enhances interpretability and can improve parametric efficiency without compromising distributional flexibility for complex data.