IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i6p955-d773067.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/6/955/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/6/955/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Klein, Ingo, 2012. "Quasi-arithmetische Mittelwerte und Normalverteilung," Discussion Papers 89/2010, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    2. García, V.J. & Gómez-Déniz, E. & Vázquez-Polo, F.J., 2010. "A new skew generalization of the normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 2021-2034, August.
    3. Arthur Pewsey & Héctor Gómez & Heleno Bolfarine, 2012. "Likelihood-based inference for power distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 775-789, December.
    4. Guillermo Martínez-Flórez & Carlos Barrera-Causil & Artur J. Lemonte, 2022. "Power Families of Bivariate Proportional Hazard Models," Mathematics, MDPI, vol. 10(23), pages 1-18, November.
    5. Roger Tovar-Falón & Guillermo Martínez-Flórez & Heleno Bolfarine, 2022. "Modelling Asymmetric Data by Using the Log-Gamma-Normal Regression Model," Mathematics, MDPI, vol. 10(7), pages 1-16, April.
    6. Guillermo Martínez-Flórez & Diego I. Gallardo & Osvaldo Venegas & Heleno Bolfarine & Héctor W. Gómez, 2021. "Flexible Power-Normal Models with Applications," Mathematics, MDPI, vol. 9(24), pages 1-15, December.
    7. Guillermo Martínez-Flórez & Roger Tovar-Falón & Heleno Bolfarine, 2023. "The Log-Bimodal Asymmetric Generalized Gaussian Model with Application to Positive Data," Mathematics, MDPI, vol. 11(16), pages 1-14, August.
    8. Kleijnen, J.P.C., 2007. "Simulation Experiments in Practice : Statistical Design and Regression Analysis," Discussion Paper 2007-30, Tilburg University, Center for Economic Research.
    9. R. N. Rattihalli, 2023. "A Class of Multivariate Power Skew Symmetric Distributions: Properties and Inference for the Power-Parameter," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1356-1393, August.
    10. Kleijnen, J.P.C., 2006. "White Noise Assumptions Revisited : Regression Models and Statistical Designs for Simulation Practice," Other publications TiSEM d8c37ad3-f9a5-4824-986d-2, Tilburg University, School of Economics and Management.
    11. Proietti, Tommaso & Lütkepohl, Helmut, 2013. "Does the Box–Cox transformation help in forecasting macroeconomic time series?," International Journal of Forecasting, Elsevier, vol. 29(1), pages 88-99.
    12. Tingguo Zheng & Tao Song, 2014. "A Realized Stochastic Volatility Model With Box-Cox Transformation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 593-605, October.
    13. Guillermo Martínez-Flórez & Heleno Bolfarine & Héctor Gómez, 2015. "Doubly censored power-normal regression models with inflation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 265-286, June.
    14. Artur J. Lemonte & Jorge L. Bazán, 2018. "New links for binary regression: an application to coca cultivation in Peru," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 597-617, September.
    15. Lemonte, Artur J., 2013. "A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 149-170.
    16. Guillermo Martínez-Flórez & Roger Tovar-Falón & Víctor Leiva & Cecilia Castro, 2024. "Skew-Normal Inflated Models: Mathematical Characterization and Applications to Medical Data with Excess of Zeros and Ones," Mathematics, MDPI, vol. 12(16), pages 1-23, August.
    17. Javier Martínez Torres & Jorge Pastor Pérez & Joaquín Sancho Val & Aonghus McNabola & Miguel Martínez Comesaña & John Gallagher, 2020. "A Functional Data Analysis Approach for the Detection of Air Pollution Episodes and Outliers: A Case Study in Dublin, Ireland," Mathematics, MDPI, vol. 8(2), pages 1-19, February.
    18. Daniel A. Griffith, 2022. "Reciprocal Data Transformations and Their Back-Transforms," Stats, MDPI, vol. 5(3), pages 1-24, July.
    19. Emilio Gómez-Déniz & Barry C. Arnold & José M. Sarabia & Héctor W. Gómez, 2021. "Properties and Applications of a New Family of Skew Distributions," Mathematics, MDPI, vol. 9(1), pages 1-18, January.
    20. Xurxo Rigueira & María Araújo & Javier Martínez & Paulino José García-Nieto & Iago Ocarranza, 2022. "Functional Data Analysis for the Detection of Outliers and Study of the Effects of the COVID-19 Pandemic on Air Quality: A Case Study in Gijón, Spain," Mathematics, MDPI, vol. 10(14), pages 1-27, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:955-:d:773067. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.