Bias-Correction Methods for the Unit Exponential Distribution and Applications

Hua Xin, Yuhlong Lio, Ya-Yen Fan and Tzong-Ru Tsai ()
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Hua Xin: School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, China
Yuhlong Lio: Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA
Ya-Yen Fan: Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan
Tzong-Ru Tsai: Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan

Mathematics, 2024, vol. 12, issue 12, 1-17

Abstract: 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.

Keywords: bias; maximum likelihood estimation; moment; Newton–Raphson algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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