On the MLE of the Waring distribution

查看全文 作　　者：Yanlin [1]Tang;Jinglong [2]Wang;Zhongyi [2]Zhu 机构地区：[1]KLATASDS-MOE,School of Statistics,East China Normal University Shanghai,People's Republic of China;[2]Department of Statistics and Data Science,Fudan University,Shanghai,People's Republic of China 出　　处：《Statistical Theory and Related Fields》索引2023年第7卷第2期,共15页 基　　金：This work is partially supported by National Natural Science Foundation of China[Grant Numbers 11671096,11690013,11731011,11871376];Natural Science Foundation of Shanghai[Grant Number 21ZR1420700]. 摘　　要：The two-parameter Waring is an important heavy-tailed discrete distribution,which extends the famous Yule Simon distribution and provides more flexibility when modelling the data.The commonly used EFF(Expectation-First Frequency)for parameter estimation can only be applied when the first moment exists,and it only uses the information of the expectation and the first frequency,which is not as efficient as the maximum likelihood estimator(MLE).However,the MLE may not exist for some sample data.We apply the profle method to the log-likelihood function and derive the necessary and sufficient Conditions for the existence of the MLE of the Waring parameters.We use extensive simulation studies to compare the MLE and EFF methods,and the goodness-of-fit comparison with the Yule Simon distribution.We also apply the Waring distribution to fit an insurance data. 关 键 词：Maximum lkelihood estimator heay-tailed discrete distribution Waring distribution