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The mean resultant length of the spherically projected normal distribution

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  • Presnell, Brett
  • Rumcheva, Pavlina

Abstract

We derive a closed-form expression for the mean resultant length of the d-dimensional projected normal distribution and provide graphical comparisons of the projected normal and Fisher-von Mises distributions in three and four dimensions.

Suggested Citation

  • Presnell, Brett & Rumcheva, Pavlina, 2008. "The mean resultant length of the spherically projected normal distribution," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 557-563, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:5:p:557-563
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    References listed on IDEAS

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    1. K. V. Mardia, 1999. "Directional statistics and shape analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 949-957.
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    Cited by:

    1. Christopher S. Withers & Saralees Nadarajah, 2011. "New Expressions for Repeated Upper Tail Integrals of the Normal Distribution," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 855-871, December.
    2. Yijian Chuan & Lan Wu, 2019. "Centralizing-Unitizing Standardized High-Dimensional Directional Statistics and Its Applications in Finance," Papers 1912.10709, arXiv.org, revised Aug 2020.
    3. Nuñez-Antonio, Gabriel & Gutiérrez-Peña, Eduardo, 2014. "A Bayesian model for longitudinal circular data based on the projected normal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 506-519.

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