Extreme changes in weather across the globe are substantially responsible to incite calamities like drought. While we cannot control weather, it is a harsh reality that we cannot stop droughts. However, the consequent detriments can discerningly be reduced to a tolerable limit by developing long term rational planning. To attain this objective, probability models are imperative as they measure and analyze the variation in the random phenomena in an orderly way and help to collect useful information leading toward meaningful predictions. In this paper, an explicit distribution based on the convolution of stochastic variables is derived from the Bivariate Affine-Linear Exponential (BALE) distribution to model the interarrival time of drought. The proposed model follows the trend of the observed drought data of the Colorado Drainage Basin in the USA that provides the rationale for its reliable forecasting. The return periods are also estimated for the interarrival time of drought to obtain important inferences for future planning. Finally, some quantiles associated with this model are provided, which are useful to predict changes in the interarrival times of droughts.

全球天气的极端变化是引发干旱等灾难的主要原因。虽然我们无法控制天气，但我们不能阻止干旱是一个严酷的现实。但是，通过制定长期合理的计划，可以将由此产生的危害降低到可以容忍的极限。为了实现这一目标，概率模型势在必行，因为它们有序地测量和分析随机现象的变化，并有助于收集有用的信息，从而进行有意义的预测。本文从二元仿射线性指数（BALE）分布推导了基于随机变量卷积的显式分布，以模拟干旱的到达时间。所提出的模型遵循了美国科罗拉多流域干旱观测数据的趋势，这为可靠的预报提供了依据。还估计干旱的到来时间的返回期，以获得对未来计划的重要推论。最后，提供了与此模型相关的一些分位数，这些分位数可用于预测干旱的到达间隔时间的变化。