In this article, we introduce a flexible cylindrical distribution for modeling and analysis of dependent extremal and directional observations. The distribution can be used to investigate the connection between two related phenomena, such as the daily fastest wind speed and its direction. The proposed model is applicable for the analysis of a wide variety of cylindrical data, including datasets with asymmetrically distributed directional observations. The model enjoys the advantages of interpretable model parameters, known marginal and conditional distributions, and a practical test for independence. Our simulation study shows that maximum likelihood estimators of the model parameters maintain desired finite sample properties. The distribution is then used to characterize the joint behavior of atmospheric variables in the context of wildfires or bushfires.

在本文中，我们介绍了一种灵活的圆柱分布，用于对相关极值和方向观测进行建模和分析。该分布可用于研究两种相关现象之间的联系，例如每日最快风速及其方向。所提出的模型适用于分析各种圆柱数据，包括具有非对称分布方向观测的数据集。该模型具有可解释的模型参数、已知的边际和条件分布以及独立性的实际测试的优点。我们的模拟研究表明，模型参数的最大似然估计量保持所需的有限样本属性。