This study evaluated probability distributions for modeling time series with abrupt structural changes. The Pearson type VII distribution, with an adjustable shape parameter $b$, proved versatile. The generalized Laplace distribution performed similarly to the Pearson model, occasionally surpassing it in terms of likelihood and AIC. Mixture models, including the mixture of $\delta$-function and Gaussian distribution, showed potential but were less stable. Pearson type VII and extended Laplace models were deemed more reliable for general cases. Model selection depends on data characteristics and goals.

翻译：本研究评估了用于建模具有突变结构变化的时间序列的概率分布。具有可调形状参数$b$的Pearson VII型分布被证明具有广泛的适用性。广义拉普拉斯分布的表现与Pearson模型相似，在似然值和AIC准则方面偶尔更优。混合模型，包括$\delta$函数与高斯分布的混合，显示出潜力但稳定性较差。对于一般情况，Pearson VII型和扩展拉普拉斯模型被认为更可靠。模型选择取决于数据特征和研究目标。