Knowing the temporal and spatial variability of the probability of rainfall occurrence is indispensable for the planning and management of agricultural and agroindustrial activities. This study aims to evaluate the applicability of four cumulative distribution functions (CDFs; exponential, two‐parameter exponential, mixed exponential, and gamma) to estimate the probability of daily rainfall in the Tocantins–Araguaia hydrographic region (TAHR). The CDFs were applied to 196 rainfall gauge stations distributed in three homogeneous regions (HRs) of rainfall in the TAHR. In relation to the CDFs, the Kolmogorov–Smirnov test and the probability–probability plot showed that the mixed exponential best adhered to the observed data for most of the months of the year in the three HRs that were analyzed. In the few months that this function did not have a good statistical performance, the gamma function was the one with the best fit quality. This study can be used as a guide for studies in other river basins in Brazil and around the world to estimate CDFs of daily rainfall.

中文翻译：

---

巴西亚马逊河Tocantins-Araguaia水文地区日降水量的累积分布函数

知道降雨发生概率的时间和空间变异性对于农业和农用工业活动的计划和管理是必不可少的。这项研究旨在评估四个累积分布函数（CDF；指数，两参数指数，混合指数和伽马）的适用性，以估算Tocantins-Araguaia水文学区（TAHR）每日降雨的可能性。CDF被应用到分布在TAHR中三个均匀区域（HRs）的196个雨量计站。关于CDF，Kolmogorov-Smirnov检验和概率-概率图显示，在分析的三个HR中，混合指数的最佳拟合在一年中的大部分月份都符合观察到的数据。在几个月前，该函数的统计性能不佳，伽马函数是拟合质量最好的函数。该研究可以用作在巴西和世界其他地区进行的研究的指南，以估算每日降雨量的CDF。