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Bias Correction Method for Log-Power-Normal Distribution

Author

Listed:
  • Tzong-Ru Tsai

    (Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan)

  • 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)

  • Che-Pin Cheng

    (Department of Information Management, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan)

Abstract

The log-power-normal distribution is a generalized version of the log-normal distribution. The maximum likelihood estimation method is the most popular method to obtain the estimates of the log-power-normal distribution parameters. In this article, we investigate the performance of the maximum likelihood estimation method for point and interval inferences. Moreover, a simple method that has less impact from the subjective selection of the initial solutions to the model parameters is proposed. The bootstrap bias correction method is used to enhance the estimation performance of the maximum likelihood estimation method. The proposed bias correction method is simple for use. Monte Carlo simulations are conducted to check the quality of the proposed bias correction method. The simulation results indicate that the proposed bias correction method can improve the performance of the maximum likelihood estimation method with a smaller bias and provide a coverage probability close to the nominal confidence coefficient. Two real examples about the air pollution and cement’s concrete strength are used for illustration.

Suggested Citation

  • Tzong-Ru Tsai & Yuhlong Lio & Ya-Yen Fan & Che-Pin Cheng, 2022. "Bias Correction Method for Log-Power-Normal Distribution," Mathematics, MDPI, vol. 10(6), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:955-:d:773067
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    References listed on IDEAS

    as
    1. Rameshwar Gupta & Ramesh Gupta, 2008. "Analyzing skewed data by power normal model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 197-210, May.
    2. Freeman, Jade & Modarres, Reza, 2006. "Inverse Box-Cox: The power-normal distribution," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 764-772, April.
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