The point process (PP) modelling approach is considered a more elegant alternative of extreme value analysis. This is because of its capability in modelling both the frequency and intensity rates of the occurrence of extremes. In this paper, we demonstrate the use of the PP modelling approach in which stationary and non-stationary models are used in modelling average maximum daily temperature (AMDT) in South Africa. The data constitutes average daily temperature observations that are collected by the South African Weather Services over the period 1 January 2000 to 30 August 2010. This study is interested on the occurrence of extreme high temperature and because of that the data for non-winter season (1 September to 30 April) of each year is used. A penalised regression cubic smoothing spline function is used for non-linear detrending of the data and determining a fixed threshold above which excesses are extracted and used. An extremal mixture model is then fitted to determine a threshold in which a boundary corrected kernel density is fitted to the bulk model and a generalised Pareto distribution (GPD) fitted to the tail of the distribution. The data exhibits properties of short-range dependence and strong seasonality, leading to declustering. An interval estimator method is used to decluster data for the purpose of fitting PP models to cluster maxima. The models that are used in this paper are nested and, as a result, likelihood ratio tests are conducted using the deviance statistic. The tests support the fit of the stationary PP model. We further fitted the stationary GPD and used the formal tests which are the Cramér-von Mises test and the Anderson-Darling test to diagnose fit. These tests and the diagnostic plots support fit of the stationary GPD to cluster maxima. Uncertainty of the estimates of GPD parameters is assessed in this paper using bootstrap re-sampling approach. The stationary PP model was used with the reparameterisation approach to determine frequency of the occurrence of extremely hot days, which are found to be 15 times per year. The modelling framework and results of this study are important to power utility companies in scheduling and dispatching electricity to customers during a hot spell.

点过程（PP）建模方法被认为是极值分析的一种更优雅的替代方法。这是因为它具有对极端现象发生的频率和强度速率进行建模的能力。在本文中，我们演示了PP建模方法的使用，在该模型中，使用固定模型和非固定模型对南非的平均最高日温度（AMDT）进行建模。该数据构成了南非气象局在2000年1月1日至2010年8月30日期间收集的每日平均温度观测值。该研究对极端高温的发生感兴趣，因为该数据为非冬季季节（使用每年的9月1日至4月30日）。惩罚回归三次平滑样条函数用于数据的非线性去趋势和确定固定阈值，超过该阈值将提取并使用超出部分。然后拟合极值混合模型以确定阈值，在该阈值中将边界校正的内核密度拟合到体模型，而广义帕累托分布（GPD）拟合到分布的尾部。数据显示出短距离依赖性和强烈的季节性特征，导致数据聚积。为了将PP模型拟合到最大聚类，使用了间隔估计器方法对数据进行聚类。本文中使用的模型是嵌套的，因此，使用偏差统计量进行似然比检验。测试支持固定PP模型的拟合。我们进一步对固定式GPD进行了拟合，并使用了Cramér-vonMises检验和Anderson-Darling检验等形式的测试来诊断拟合。这些测试和诊断图支持固定GPD拟合聚类最大值。本文使用自举重采样方法评估了GPD参数估计值的不确定性。固定PP模型与重新参数化方法一起使用，可以确定极端炎热天气的发生频率，每年被发现为15次。这项研究的建模框架和结果对电力公司在热点期间调度和向客户分配电力至关重要。这些测试和诊断图支持固定GPD拟合聚类最大值。本文使用自举重采样方法评估了GPD参数估计值的不确定性。固定PP模型与重新参数化方法一起使用，可以确定极端炎热天气的发生频率，每年被发现为15次。这项研究的建模框架和结果对电力公司在热点期间调度和向客户分配电力至关重要。这些测试和诊断图支持固定GPD拟合聚类最大值。本文使用自举重采样方法评估了GPD参数估计值的不确定性。固定PP模型与重新参数化方法一起使用，可以确定极端炎热天气的发生频率，每年被发现为15次。这项研究的建模框架和结果对电力公司在热点期间调度和向客户分配电力至关重要。