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Three Occurrences of the Hyperbolic-Secant Distribution

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  • Peng Ding

Abstract

Although it is the generator distribution of the sixth natural exponential family with quadratic variance function, the Hyperbolic-Secant (HS) distribution is much less known than other distributions in the exponential families. Its lack of familiarity is due to its isolation from many widely used statistical models. We fill in the gap by showing three examples naturally generating the HS distribution, including Fisher's analysis of similarity between twins, the Jeffreys' prior for contingency tables, and invalid instrumental variables.

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  • Peng Ding, 2014. "Three Occurrences of the Hyperbolic-Secant Distribution," The American Statistician, Taylor & Francis Journals, vol. 68(1), pages 32-35, February.
    • Handle: RePEc:taf:amstat:v:68:y:2014:i:1:p:32-35
    DOI: 10.1080/00031305.2013.867902
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    References listed on IDEAS

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    1. Morris, Carl N. & Lock, Kari F., 2009. "Unifying the Named Natural Exponential Families and Their Relatives," The American Statistician, American Statistical Association, vol. 63(3), pages 247-253.
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    Cited by:

    1. Pan, Yan & Duan, Fabing & Xu, Liyan & Chapeau-Blondeau, François, 2019. "Benefits of noise in M-estimators: Optimal noise level and probability density," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    2. Piero Quatto & Gianmarco Vacca & Maria Grazia Zoia, 2021. "Modeling Portfolios with Leptokurtic and Dependent Risk Factors," Papers 2106.04218, arXiv.org.
    3. 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.

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