Modeling rainfall data and analyzing precipitation variability are accurately critical for managing water resources. Generally, rainfall is one of the most important inputs in model fitting based on probability distribution functions. The probability functions provide the possibility of estimation rainfall variability within a specific range. But in many situations, especially in the low rainfall regions, there will be many zero rainfall values. In these cases, the common distributions applied in the literatures cannot be used for modeling those data since statistically they are defined on positive range values. To overcome this problem an edition on the common probability functions should be implemented. The aim of this study is to introduce the zero-adjusted models (ZAM) and then applying these models on monthly rainfall using 46 years of data from 25 stations in semi-arid, arid and extra-arid regions of Iran. The models that will be used through this study, are the zero-adjusted gamma (ZAGA), zero-adjusted Weibull (ZAWEI), zero-adjusted inverse Gaussian (ZAIG), zero-adjusted log-logistic (ZALL) and zero-adjusted log-normal (ZALN). For selecting the best fitted model some numerical validation methods such as the AIC, the BIC and the K–S test are used. Bedsides the numerical methods, some graphical aspects such as PDF, CDF, and Q–Q plots have been served. The results show that the ZAWEI model is suitable for the extra-arid regions, while the ZAGA model has a better performance in the semi-arid and arid regions. This study attempts to provide the technique of using ZA models for the rainfall data in the low-rainfall region and can be considered as a foundation of using these statistical models. The ZAMs can be applied to the rainfall data, and to classify (or cluster) the rainfall regimes, especially for the semi-arid, arid and extra-arid regions of Iran. Also, these probability models can be considered as decision-support tools for decision-makers to manage the water and agricultural resources as well as food reserves with assessing different scenarios in these regions.

中文翻译：

---

在半干旱、干旱和额外干旱地区使用零调整模型对月降雨数据进行建模

建模降雨数据和分析降水变异性对于管理水资源至关重要。通常，降雨量是基于概率分布函数的模型拟合中最重要的输入之一。概率函数提供了在特定范围内估计降雨变化的可能性。但是在很多情况下，特别是在低降雨量地区，会出现很多零降雨值。在这些情况下，文献中应用的常见分布不能用于对这些数据进行建模，因为在统计上它们是在正范围值上定义的。为了克服这个问题，应该实施一个关于公共概率函数的版本。本研究的目的是引入零调整模型 (ZAM)，然后使用来自伊朗半干旱、干旱和超干旱地区 25 个站点的 46 年数据，将这些模型应用于月降雨量。本研究将使用的模型是零调整伽玛 (ZAG​​A)、零调整威布尔 (ZAWEI)、零调整逆高斯 (ZAIG)、零调整对数逻辑 (ZALL) 和零调整对数正态 (ZALN)。为了选择最佳拟合模型，使用了一些数值验证方法，例如 AIC、BIC 和 K-S 检验。除了数值方法之外，还提供了一些图形方面，例如 PDF、CDF 和 Q-Q 图。结果表明，ZAWEI模型适用于极端干旱地区，而ZAGA模型在半干旱和干旱地区具有较好的性能。本研究试图为低降雨区的降雨数据提供使用ZA模型的技术，可作为使用这些统计模型的基础。ZAM 可应用于降雨数据，并对降雨情况进行分类（或聚类），特别是对于伊朗的半干旱、干旱和超干旱地区。此外，这些概率模型可以被视为决策者的决策支持工具，用于管理水资源和农业资源以及粮食储备，并评估这些地区的不同情景。伊朗的干旱和极端干旱地区。此外，这些概率模型可以被视为决策者的决策支持工具，用于管理水资源和农业资源以及粮食储备，并评估这些地区的不同情景。伊朗的干旱和极端干旱地区。此外，这些概率模型可以被视为决策者的决策支持工具，用于管理水资源和农业资源以及粮食储备，并评估这些地区的不同情景。