In extreme values, the block maxima procedure can provide a few observations to perform the inference using the generalized extreme values (GEV) distribution. In this case, an interesting alternative is considered to use the r-largest order statistics ($GE{V}_r$). This study aims in obtaining the posterior distribution for the $GE{V}_r$ based on the Bayesian estimation using the Markov chain Monte Carlo method and the Metropolis–Hastings algorithm procedure. The novelty of this study is the introduction of a dynamic linear seasonal model to capture the parameters of the $GE{V}_r$ distribution over time. Also, we propose an adapted dynamic criterion for choosing the optimal value of r for each time point. The proposed model exhibits good performance in the simulations. Moreover, the application of the proposed model is performed on the dataset of daily maxima temperature (${}^{\circ }\mathrm{C}$) in Teresina, Piaui, Brazil.

在极值中，块最大值过程可以提供一些观察结果，以使用广义极值 (GEV) 分布执行推理。在这种情况下，一个有趣的替代方案被认为是使用r -最大阶统计（$G乙{五}_r$）。本研究旨在获得$G乙{五}_r$基于使用马尔可夫链蒙特卡罗方法和 Metropolis-Hastings 算法程序的贝叶斯估计。本研究的新颖之处在于引入了动态线性季节性模型来捕获$G乙{五}_r$随时间分布。此外，我们提出了一个适应的动态标准，用于为每个时间点选择r的最佳值。所提出的模型在模拟中表现出良好的性能。此外，该模型的应用是在日最高温度数据集（${}^{\circ }\mathrm{C}$) 在巴西皮奥伊的特雷西纳。