We propose a new generalized linear model for modeling multivariate events $(N,X,Y)$, where $N$ is the duration, $X$ is the magnitude, and $Y$ is the maximum of the event. Such events arise, for example, when a process is observed above or below a threshold. Examples include heat waves, flood, draught, or market growth or decline periods. The model is flexible to include different covariates for different parameters. In addition, we propose a new method for checking the goodness of fit (validation) of the model to data. Our goodness of fit methods are based on distributional fit of appropriately transformed data. We include a data example from finance to illustrate the modeling potential of this new generalized linear model.

我们提出了一种新的广义线性模型来建模多变量事件 $(N,X,是)$， 在哪里 $N$ 是持续时间， $X$ 是大小，并且 $是$是事件的最大值。例如，当观察到的过程高于或低于阈值时，就会出现此类事件。示例包括热浪、洪水、干旱或市场增长或衰退期。该模型可以灵活地为不同的参数包含不同的协变量。此外，我们提出了一种新的方法来检查模型对数据的拟合（验证）的好坏。我们的拟合优度方法基于适当转换数据的分布拟合。我们包括一个来自金融的数据示例来说明这种新的广义线性模型的建模潜力。