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On the Folded Normal Distribution

Author

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  • Tsagris, Michail
  • Beneki, Christina
  • Hassani, Hossein

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

  • Tsagris, Michail & Beneki, Christina & Hassani, Hossein, 2013. "On the Folded Normal Distribution," MPRA Paper 53748, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:53748
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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:

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    3. 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).
    4. 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).
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    6. 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.
    7. 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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