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Quasi logistic distributions and Gaussian scale mixing

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Virtualconference
Authors : Letac, Gerard (Author of the conference)
CIRM (Publisher )

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Abstract : A quasi logistic distribution on the real line has density proportional to $(cosh x+cos a)^{-1}$ if $V> 0$ and $Z$ with standard normal law are independent, we say that $\sqrt{V}$ has a quasi Kolmogorov distribution if $Z\sqrt{V}$ is quasi logistic. We study the numerous properties of these generalizations of the logistic and Kolmogorov laws.

Keywords : Quasi logistic laws; quasi Kolmogorov laws; scale Gaussian mixtures

MSC Codes :
33E05 - Elliptic functions and integrals
60E07 - Infinitely divisible distributions; stable distributions
62E10 - Characterization and structure theory

Additional resources :
https://www.cirm-math.fr/RepOrga/2146/Slides/Letac.pdf

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 15/06/2020
    Conference Date : 02/06/2020
    Subseries : Research talks
    arXiv category : Statistics Theory
    Mathematical Area(s) : Probability & Statistics
    Format : MP4 (.mp4) - HD
    Video Time : 00:57:07
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/ 2020-06-02_Letac.mp4

Information on the Event

Event Title : Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2
Event Organizers : Bogdan, Malgorzata ; Graczyk, Piotr ; Panloup, Fabien ; Proïa, Frédéric ; Roquain, Etienne
Dates : 15/06/2020 - 19/06/2020
Event Year : 2020
Event URL : https://www.cirm-math.com/cirm-virtual-...

Citation Data

DOI : 10.24350/CIRM.V.19641803
Cite this video as: Letac, Gerard (2020). Quasi logistic distributions and Gaussian scale mixing. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19641803
URI : http://dx.doi.org/10.24350/CIRM.V.19641803

See Also

Bibliography

  • ANDREWS, David F. et MALLOWS, Colin L. Scale mixtures of normal distributions. Journal of the Royal Statistical Society: Series B (Methodological), 1974, vol. 36, no 1, p. 99-102. - https://doi.org/10.1111/j.2517-6161.1974.tb00989.x

  • LETAC, Gérard et MASSAM, Hélène. Gaussian approximation of Gaussian scale mixture. arXiv preprint arXiv:1810.02036, 2018. - https://arxiv.org/abs/1810.02036

  • MONAHAN, John H. et STEFANSKI, Leonard A. Normal scale mixture approximations to the logistic distribution with applications. North Carolina State University. Dept. of Statistics, 1989. -

  • STEFANSKI, Leonard A. A normal scale mixture representation of the logistic distribution. Statistics & Probability Letters, 1991, vol. 11, no 1, p. 69-70. - https://doi.org/10.1016/0167-7152(91)90181-P

  • WEST, Mike. On scale mixtures of normal distributions. Biometrika, 1987, vol. 74, no 3, p. 646-648. - https://doi.org/10.1093/biomet/74.3.646



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