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Dependence Modeling

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Exact distributions of order statistics of dependent random variables from ln,p-symmetric sample distributions, n ∈ {3,4}

K. Müller
  • Corresponding author
  • University of Rostock, Institute of Mathematics, Ulmenstraße 69, Haus 3, 18057 Rostock, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ W.-D. Richter
  • Corresponding author
  • University of Rostock, Institute of Mathematics, Ulmenstraße 69, Haus 3, 18057 Rostock, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-02-22 | DOI: https://doi.org/10.1515/demo-2016-0001

Abstract

Integral representations of the exact distributions of order statistics are derived in a geometric way when three or four random variables depend on each other as the components of continuous ln,psymmetrically distributed random vectors do, n ∈ {3,4}, p > 0. Once the representations are implemented in a computer program, it is easy to change the density generator of the ln,p-symmetric distribution with another one for newly evaluating the distribution of interest. For two groups of stock exchange index residuals, maximum distributions are compared under dependence and independence modeling.

Keywords: density generator; extreme value statistics; geometric measure representation; p-generalized Gaussian and Laplace distributions; financial data analysis

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About the article

Received: 2015-10-12

Accepted: 2016-02-05

Published Online: 2016-02-22


Citation Information: Dependence Modeling, Volume 4, Issue 1, ISSN (Online) 2300-2298, DOI: https://doi.org/10.1515/demo-2016-0001.

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© 2016 K. Müller and W.-D. Richter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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