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On the Folded Normal Distribution

Author

Listed:
  • Michail Tsagris

    (School of Mathematical Sciences, University of Nottingham, NG7 2RD, UK)

  • Christina Beneki

    (School of Business and Economics, TEI of Ionian Islands, 31100 Lefkada, Greece)

  • Hossein Hassani

    (Statistical Research Centre, Executive Business Centre, Bournemouth University, BH8 8EB, UK)

Abstract

The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback–Leibler from the normal and half normal distributions are approximated using Taylor series. The accuracy of the results are also assessed using different criteria. The maximum likelihood estimates and confidence intervals for the parameters are obtained using the asymptotic theory and bootstrap method. The coverage of the confidence intervals is also examined.

Suggested Citation

  • Michail Tsagris & Christina Beneki & Hossein Hassani, 2014. "On the Folded Normal Distribution," Mathematics, MDPI, vol. 2(1), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:2:y:2014:i:1:p:12-28:d:32965
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    References listed on IDEAS

    as
    1. Psarakis, Stelios & Panaretos, John, 2001. "On Some Bivariate Extensions of the Folded Normal and the Folded-T Distributions," MPRA Paper 6383, University Library of Munich, Germany.
    2. Yee, Thomas W., 2010. "The VGAM Package for Categorical Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i10).
    3. Psarakis, Stelios & Panaretos, John, 1990. "The Folded t Distribution," MPRA Paper 6257, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Wen Shi & Xi Chen & Jennifer Shang, 2019. "An Efficient Morris Method-Based Framework for Simulation Factor Screening," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 745-770, October.
    2. Mardia, Kanti V. & Wiechers, Henrik & Eltzner, Benjamin & Huckemann, Stephan F., 2022. "Principal component analysis and clustering on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Shi, Yan & Lu, Zhenzhou & He, Ruyang & Zhou, Yicheng & Chen, Siyu, 2020. "A novel learning function based on Kriging for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    4. Budnik, Katarzyna & Rünstler, Gerhard, 2020. "Identifying structural VARs from sparse narrative instruments: dynamic effects of U.S. macroprudential policies," Working Paper Series 2353, European Central Bank.
    5. Maria-Teresa Bosch-Badia & Joan Montllor-Serrats & Maria-Antonia Tarrazon-Rodon, 2020. "Risk Analysis through the Half-Normal Distribution," Mathematics, MDPI, vol. 8(11), pages 1-27, November.
    6. Qiwei Xie & Linda L. Zhang & Haichao Shang & Ali Emrouznejad & Yongjun Li, 2021. "Evaluating performance of super-efficiency models in ranking efficient decision-making units based on Monte Carlo simulations," Annals of Operations Research, Springer, vol. 305(1), pages 273-323, October.

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    More about this item

    Keywords

    folded normal distribution; entropy; Kullback–Leibler; maximum likelihood estimates;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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