IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v76y2006i8p764-772.html
   My bibliography  Save this article

Inverse Box-Cox: The power-normal distribution

Author

Listed:
  • Freeman, Jade
  • Modarres, Reza

Abstract

Box-Cox transformation system produces the power normal (PN) family, whose members include normal and lognormal distributions. We study the moments of PN and obtain expressions for its mean and variance. The quantile functions and a quantile measure of skewness are discussed to show that the PN family is ordered with respect to the transformation parameter. Chebyshev-Hermite polynomials are used to show that the correlation coefficient is smaller in the PN scale than the original scale. We use the Fréchet bounds to obtain expressions for the lower and upper bounds of the correlation coefficient. A numerical routine is used to compute the bounds. The transformation parameter of the PN family is used to investigate the effects of model uncertainty on the upper quantile estimates.

Suggested Citation

  • Freeman, Jade & Modarres, Reza, 2006. "Inverse Box-Cox: The power-normal distribution," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 764-772, April.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:8:p:764-772
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(05)00386-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Charles N. Haas, 1997. "Importance of Distributional Form in Characterizing Inputs to Monte Carlo Risk Assessments," Risk Analysis, John Wiley & Sons, vol. 17(1), pages 107-113, February.
    2. Modarres, Reza & Nayak, Tapan K. & Gastwirth, Joseph L., 2002. "Estimation of upper quantiles under model and parameter uncertainty," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 529-554, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Klein, Ingo, 2012. "Quasi-arithmetische Mittelwerte und Normalverteilung," Discussion Papers 89/2010, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    3. Kleijnen, J.P.C., 2007. "Simulation Experiments in Practice : Statistical Design and Regression Analysis," Discussion Paper 2007-09, Tilburg University, Center for Economic Research.
    4. Kleijnen, J.P.C., 2006. "White Noise Assumptions Revisited : Regression Models and Statistical Designs for Simulation Practice," Discussion Paper 2006-50, Tilburg University, Center for Economic Research.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Daniel A. Griffith, 2022. "Reciprocal Data Transformations and Their Back-Transforms," Stats, MDPI, vol. 5(3), pages 1-24, July.

    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. Uddameri, Venkatesh & Ghaseminejad, Ali & Hernandez, E. Annette, 2020. "A tiered stochastic framework for assessing crop yield loss risks due to water scarcity under different uncertainty levels," Agricultural Water Management, Elsevier, vol. 238(C).
    2. Hadi Alizadeh Noughabi, 2015. "Empirical likelihood ratio-based goodness-of-fit test for the logistic distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(9), pages 1973-1983, September.
    3. Vytaras Brazauskas & Sahadeb Upretee, 2019. "Model Efficiency and Uncertainty in Quantile Estimation of Loss Severity Distributions," Risks, MDPI, vol. 7(2), pages 1-16, May.
    4. Per Sander & Bo Bergbäck & Tomas Öberg, 2006. "Uncertain Numbers and Uncertainty in the Selection of Input Distributions—Consequences for a Probabilistic Risk Assessment of Contaminated Land," Risk Analysis, John Wiley & Sons, vol. 26(5), pages 1363-1375, October.
    5. Martí Nadal & Vikas Kumar & Marta Schuhmacher & José L. Domingo, 2008. "Applicability of a Neuroprobabilistic Integral Risk Index for the Environmental Management of Polluted Areas: A Case Study," Risk Analysis, John Wiley & Sons, vol. 28(2), pages 271-286, April.
    6. Modarres, Reza & Nayak, Tapan K. & Gastwirth, Joseph L., 2002. "Estimation of upper quantiles under model and parameter uncertainty," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 529-554, June.
    7. Charles N. Haas, 1999. "On Modeling Correlated Random Variables in Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 19(6), pages 1205-1214, December.

    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:eee:stapro:v:76:y:2006:i:8:p:764-772. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.