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Bias-Correction Methods for the Unit Exponential Distribution and Applications

Author

Listed:
  • 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)

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.

Suggested Citation

  • Hua Xin & Yuhlong Lio & Ya-Yen Fan & Tzong-Ru Tsai, 2024. "Bias-Correction Methods for the Unit Exponential Distribution and Applications," Mathematics, MDPI, vol. 12(12), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1828-:d:1413518
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    References listed on IDEAS

    as
    1. Hassan S. Bakouch & Tassaddaq Hussain & Marina Tošić & Vladica S. Stojanović & Najla Qarmalah, 2023. "Unit Exponential Probability Distribution: Characterization and Applications in Environmental and Engineering Data Modeling," Mathematics, MDPI, vol. 11(19), pages 1-22, October.
    2. Luiz R. Nakamura & Pedro H. R. Cerqueira & Thiago G. Ramires & Rodrigo R. Pescim & R. A. Rigby & Dimitrios M. Stasinopoulos, 2019. "A new continuous distribution on the unit interval applied to modelling the points ratio of football teams," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(3), pages 416-431, February.
    3. Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 169-176, February.
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