变形广义极值分布的参数估计及实例分析

Parameter Estimation and Case Analysis of Generalized Extreme Value Distribution

本文通过对广义极值(GEV)分布运用二次秩变形映射导出变形的广义极值(TGEV)分布的概率分布函数和概率密度函数,并对TGEV分布的参数进行了MLE和矩估计.用R语言中的optim函数对TGEV分布的参数做了MLE估计,并对此估计方法的偏差和均方误差做了模拟,说明对于TGEV分布来说,MLE估计方法效果很好.最后对变形广义极值分布进行实例分析,给出了TGEV分布拟合的结果,得到分位数及其置信区间的估计,并讨论了所得结果的实际意义.

Based on the generalized extreme value （GEV） distribution, using the quadratic Rank Transmutation Map, we derive the probability distribution function and probability density function of the transmuted generalized extreme value （TGEV） distribution, and provide MLE and the moment estimator from TGEV distribution. The optim function of R language is used to do MLE of TGEV distribution and to simulate for bias and mean square error of MLE methods. The MLE method is better for the TGEV distribution. Finally, the transmuted generalized extreme valus distribution is applied in a case study, giving the TGEV distribution fitting results, obtaining estimation of quantile and confidence intervals, and discussing the practical significance of the results.