论文标题
灵活的牙龈分布：用于推理模式的新模型
The flexible Gumbel distribution: A new model for inference about the mode
论文作者
论文摘要
由模式和其他三个参数索引的新的非峰分布家族是从牙龈分布的最大值和最小值的牙龈分布的混合物中得出的。探索了所提出的分布的属性，包括模型可识别性和灵活性，以捕获在广泛范围内显示出不同方向的重尾数据。频繁主义者和贝叶斯方法都是为了推断新分布中的参数而开发的。进行了模拟研究以证明两种方法的令人满意的性能。通过将所提出的模型拟合到模拟水文学应用程序中的数据和数据，这表明所提出的柔性分布特别适用于包含两个方向上的极值的数据，模式为感兴趣的位置参数。使用所提出的单峰分布，可以轻松地制定有关给定协变量响应模式的回归模型。我们将此模型应用于犯罪学应用程序的数据，以揭示异常值遮盖的有趣数据功能。用于实施研究中所有考虑推理方法的计算机程序可在https://github.com/rh8liuqy/flexible_gumbel上获得。
A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are explored, including model identifiability and flexibility in capturing heavy-tailed data that exhibit different directions of skewness over a wide range. Both frequentist and Bayesian methods are developed to infer parameters in the new distribution. Simulation studies are conducted to demonstrate satisfactory performance of both methods. By fitting the proposed model to simulated data and data from an application in hydrology, it is shown that the proposed flexible distribution is especially suitable for data containing extreme values in either direction, with the mode being a location parameter of interest. Using the proposed unimodal distribution, one can easily formulate a regression model concerning the mode of a response given covariates. We apply this model to data from an application in criminology to reveal interesting data features that are obscured by outliers. Computer programs for implementing all considered inference methods in the study are available at https://github.com/rh8liuqy/flexible_Gumbel.
