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Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2

Collection Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2

Organizer(s) Bogdan, Malgorzata ; Graczyk, Piotr ; Panloup, Fabien ; Proïa, Frédéric ; Roquain, Etienne
Date(s) 15/06/2020 - 19/06/2020
linked URL https://www.cirm-math.com/cirm-virtual-event-2146.html
00:00:00 / 00:00:00
3 25

Quasi logistic distributions and Gaussian scale mixing

By Gerard Letac

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.

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Citation data

  • DOI 10.24350/CIRM.V.19641803
  • Cite this video Letac, Gerard (02/06/2020). Quasi logistic distributions and Gaussian scale mixing. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19641803
  • URL https://dx.doi.org/10.24350/CIRM.V.19641803

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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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