Statistical modeling of monthly, seasonal, or annual total rainfall is a crucial area of research in meteorology, mainly from the perspective of rainfed agriculture, where a proper assessment of the future availability of rainwater is necessary. The rainfall amount during a wet period can take any positive value and some simple (one or two-parameter) probability models supported over the positive real line that are generally used for rainfall modeling are exponential, gamma, Weibull, lognormal, Pearson Type-V/VI, log-logistic, etc., where the unknown model parameters are routinely estimated using the maximum likelihood estimator (MLE). However, the presence of outliers or extreme observations is a common issue in rainfall data and the MLEs being highly sensitive to them often leads to spurious inference. Here, we discuss a robust parameter estimation approach based on the minimum density power divergence estimator (MDPDE). We fit the above four parametric models to the areally-weighted monthly rainfall data from the 36 meteorological subdivisions of India for the years 1951-2014 and compare the fits based on MLE and the proposed optimum MDPDE; the superior performance of MDPDE is showcased for several cases. For all month-subdivision combinations, we discuss the best-fit models and the estimated median rainfall amounts.

翻译：月、季或年总降水量的统计建模是气象学中的一个重要研究领域，主要从雨养农业的角度出发，因为需要正确评估未来雨水的可用性。湿润期降水量可取任意正值，通常用于降水建模的简单（单参数或双参数）概率模型包括指数分布、伽马分布、威布尔分布、对数正态分布、皮尔逊V/VI型分布、对数逻辑斯蒂分布等，这些模型中的未知参数通常使用最大似然估计（MLE）进行常规估计。然而，降水数据中常存在异常值或极端观测值，而MLE对其高度敏感，往往会导致错误的推断。本文讨论了一种基于最小密度功率散度估计（MDPDE）的稳健参数估计方法。我们将上述四种参数模型拟合到1951-2014年印度36个气象分区的面积加权月降水量数据中，并比较基于MLE和所提出的最优MDPDE的拟合效果；通过多个案例展示了MDPDE的优越性能。针对所有月份-分区组合，我们讨论了最佳拟合模型及估计的中位数降水量。