论文标题
广义指数分布的最小密度功率发散估计
Minimum Density Power Divergence Estimation for the Generalized Exponential Distribution
论文作者
论文摘要
降雨数据的统计模型是农业气象学的一个活跃研究领域。拟合到此类数据集的最常见模型是指数，伽马，log-Normal和Weibull分布。作为其中一些模型的替代方案，Gupta和Kundu（2001年，指数指数族的指数族：伽马和Weibull分布的替代品，生物识别杂志）提出了广义指数（GE）分布。降雨（专门针对短期）数据集通常包括离群值，因此，必须进行适当的稳健参数估计过程。在这里，我们使用Basu等人开发的流行的最小密度差异估计（MDPDE）程序。 （1998年，通过最小化密度差异，生物埃当计质量来估算GE参数，可稳健有效的估计。我们得出估计方程和渐近分布的分析表达式。通过影响函数分析，我们通过分析将MDPDE与鲁棒性估计的最大似然估计进行了比较。此外，我们在分析中研究了MDPDE的渐近相对效率，以了解不同的参数设置。我们将提出的技术应用于美国德克萨斯州的一些模拟数据集和两个降雨数据集。结果表明，与大多数情况下的其他现有估计技术相比，MDPDE的性能卓越。
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.
