The generalized Pareto distribution (GPD) is a family of continuous distributions used to model the tail of the distribution to values higher than a threshold u. Despite the advantages of the GPD representation, its shape and scale parameters do not correspond to the expected value, which complicates the interpretation of regression models specified using the GPD. This study proposes a linear regression model in which the response variable is a GPD, using a new parametrization that is indexed by mean and precision parameters. The main advantage of our new parametrization is the straightforward interpretation of the regression coefficients in terms of the expectation of the positive real line response variable, as is usual in the context of generalized linear models. Furthermore, we propose a model for extreme values, in which the GPD parameters (mean and precision) are defined on the basis of a dynamic linear regression model. The novelty of the study lies in the time variation of the mean and precision parameter of the resulting distribution. The parameter estimation of these new models is performed under the Bayesian paradigm. Simulations are conducted to analyze the performance of our proposed models. Finally, the models are applied to environmental datasets (temperature datasets), illustrating their capabilities in challenging cases in extreme value theory.

广义帕累托分布（GPD）是一系列连续分布，用于将分布的尾部建模为高于阈值u的值。尽管GPD表示具有很多优点，但其形状和比例参数并不符合预期值，这使得使用GPD指定的回归模型的解释变得复杂。这项研究提出了一种线性回归模型，其中的响应变量为GPD，使用了一种新的参数化方法，该参数化方法以均值和精度参数为索引。我们新的参数化的主要优点是，根据正实线响应变量的期望，可以直接对回归系数进行解释，这在广义线性模型的情况下很常见。此外，我们提出了一个极值模型，其中GPD参数（均值和精度）是在动态线性回归模型的基础上定义的。该研究的新颖之处在于所得分布的均值和精度参数的时间变化。这些新模型的参数估计是在贝叶斯范式下进行的。进行仿真以分析我们提出的模型的性能。最后，将模型应用于环境数据集（温度数据集），以极值理论说明其在具有挑战性的情况下的功能。