Bias-Correction Methods for the Unit Exponential Distribution and Applications

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题名:	Bias-Correction Methods for the Unit Exponential Distribution and Applications
作者:	Fan, Ya-yen;Tsai, Tzong-ru
关键词:	bias;maximum likelihood estimation;moment;Newton–Raphson algorithm
日期:	2024-06-12
上传时间:	2024-08-07 12:06:45 (UTC+8)
摘要:	The bias of the maximum likelihood estimator can cause a considerable estimation error if the sample size is small. To reduce the bias of the maximum likelihood estimator under the small sample situation, the maximum likelihood and parametric bootstrap bias-correction methods are proposed in this study to obtain more reliable maximum likelihood estimators of the unit exponential distribution parameters. The procedure to implement the bias-corrected maximum likelihood estimation method is derived analytically, and the steps to obtain the bias-corrected bootstrap estimators are presented. The simulation results show that the proposed maximum likelihood bootstrap bias-correction method can significantly reduce the bias and mean squared error of the maximum likelihood estimators for most of the parameter combinations in the simulation study. A soil moisture data set and a numerical example are used for illustration.
關聯:	Mathematics 12(12),　1828
DOI:	10.3390/math12121828
显示于类别:	[統計學系暨研究所] 期刊論文

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