Statistical modeling of rainfall data is an active research area in agro-meteorology. The most common models fitted to such datasets are exponential, gamma, log-normal, and Weibull distributions. As an alternative to some of these models, the generalized exponential (GE) distribution was proposed by Gupta and Kundu (2001, Exponentiated Exponential Family: An Alternative to Gamma and Weibull Distributions, Biometrical Journal). Rainfall (specifically for short periods) datasets often include outliers, and thus, a proper robust parameter estimation procedure is necessary. Here, we use the popular minimum density power divergence estimation (MDPDE) procedure developed by Basu et al. (1998, Robust and Efficient Estimation by Minimising a Density Power Divergence, Biometrika) for estimating the GE parameters. We derive the analytical expressions for the estimating equations and asymptotic distributions. We analytically compare MDPDE with maximum likelihood estimation in terms of robustness, through an influence function analysis. Besides, we study the asymptotic relative efficiency of MDPDE analytically for different parameter settings. We apply the proposed technique to some simulated datasets and two rainfall datasets from Texas, United States. The results indicate superior performance of MDPDE compared to the other existing estimation techniques in most of the scenarios.

翻译：降雨数据的统计建模是农业气象学中的一个活跃研究领域。适用于此类数据集的常见分布模型包括指数分布、伽马分布、对数正态分布和威布尔分布。作为其中部分模型的替代方案，Gupta与Kundu（2001，《指数化指数族：伽马分布与威布尔分布的替代》，生物统计期刊）提出了广义指数（GE）分布。降雨数据集（尤其是短期降雨数据）常包含异常值，因此需要建立稳健的参数估计方法。本文采用Basu等人（1998，《通过最小化密度功率散度实现稳健高效估计》，生物统计）提出的最小密度功率散度估计（MDPDE）方法对GE参数进行估计。我们推导了估计方程及渐近分布的解析表达式，并通过影响函数分析在稳健性方面将MDPDE与极大似然估计进行解析比较。此外，我们针对不同参数设置解析研究了MDPDE的渐近相对效率。该技术被应用于模拟数据集及美国德克萨斯州的两个降雨数据集。结果表明，在多数场景下MDPDE的性能优于其他现有估计方法。