A common way of modeling the exceedance of air pollution index (API) data is to utilize the generalized Pareto distribution (GPD). The marginal GPD model is a good method for describing unhealthy API data. However, for data with multiple locations, integrating the information of GDP models from each location with a hierarchical model (HM) will provide a better result. In this study, a hierarchical-generalized Pareto model (HM-GPD) is used to integrate the information about location and seasonal effects from the marginal GPD models of hourly API exceedance data, along with the information of serial dependence at each location. The accuracy of inferences at a single site and in each season was improved by employing a Gaussian model for the random effects; this model takes advantage of the climatological structure in the data. The temporal dependence was modeled by using first-order Markov chains. This step was performed by operating the posterior draws from HM-GPD to transform the marginal models for each site to unit Frechet by using the Markov chain model likelihood. Overall, the parameters estimated from the HM-GPD are able to provide precise estimation of the return levels for each site.

建模超出空气污染指数（API）数据的常用方法是利用广义帕累托分布（GPD）。边缘GPD模型是描述不良API数据的好方法。但是，对于具有多个位置的数据，将每个位置的GDP模型信息与层次模型（HM）集成在一起将提供更好的结果。在这项研究中，使用分层广义帕累托模型（HM-GPD）来整合每小时API超出数据的边际GPD模型中有关位置和季节影响的信息，以及每个位置的序列依赖性信息。通过对随机效应采用高斯模型，可以提高单个站点和每个季节中推断的准确性。该模型利用了数据中的气候结构。时间依赖性是通过使用一阶马尔可夫链建模的。此步骤是通过操作HM-GPD的后绘制来执行的，以通过使用马尔可夫链模型可能性将每个站点的边际模型转换为单位Frechet。总体而言，从HM-GPD估计的参数能够准确估计每个站点的回报水平。