月降雨量的稳健统计建模：最小密度幂散度方法
Robust statistical modeling of monthly rainfall: The minimum density power divergence approach
AI总结：
针对降雨数据异常值导致MLE推断失真的问题，提出基于MDPDE的稳健参数估计，并在印度36个分区1951–2014年月度降雨数据上验证其优于MLE。
摘要：
月度、季节或年度降雨量数据的统计建模是气象学中的一个重要研究领域。这些模型在雨养农业中发挥着关键作用，因为该领域需要对未来雨水可用量进行恰当评估。某个多雨月份或整个雨季的降雨量可以取任意正值，而通常用于降雨建模、定义在正实数轴上的一些简单（一参数或两参数）概率模型包括指数分布、gamma分布、Weibull分布、对数正态分布、Pearson Type-V/VI分布、对数logistic分布等，其未知模型参数通常使用最大似然估计量（MLE）进行估计。然而，异常值或极端观测值的存在是降雨数据中的常见问题，而MLE对这些观测值高度敏感，往往会导致虚假推断。在此，我们讨论一种基于最小密度幂散度估计量（MDPDE）的稳健参数估计方法。我们将上述四个参数模型拟合于印度36个气象分区在1951–2014年间经去趋势处理并按面积加权的月度降雨数据，并基于MLE与所提出的最优MDPDE比较拟合效果；在若干情形中展示了MDPDE更优越的性能。对于所有月份—分区组合，我们讨论了最佳拟合模型和降雨量中位数。
英文摘要：
Statistical modeling of monthly, seasonal, or annual rainfall data is an important research area in meteorology. These models play a crucial role in rainfed agriculture, where a proper assessment of the future availability of rainwater is necessary. The rainfall amount during a rainy month or a whole rainy season} 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 detrended 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 median rainfall amounts.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
