One-Factor Lévy-Frailty Copulas with Inhomogeneous Trigger Rates

  • Janina Engel
  • Matthias SchererEmail author
  • Leonhard Spiegelberg
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 456)


A new parametric family of high-dimensional , non-exchangeable extreme-value copulas is presented. The construction is based on the Lévy-frailty construction and stems from a subfamily of the Marshall–Olkin distribution. In contrast to the classical Lévy-frailty construction, non-exchangeability is achieved by inhomogeneous trigger-rate parameters. This family is studied with respect to its distributional properties and a sampling algorithm is developed. Moreover, a new estimator for its parameters is given. The estimation strategy consists in minimizing the mean squared error of the underlying Bernstein function and certain strongly consistent estimates thereof.


Extreme-value copula Non-exchangeable Lévy-frailty model 


  1. 1.
    Bertoin J (1999) Subordinators: Examples and Applications. Springer, Berlin, HeidelbergzbMATHGoogle Scholar
  2. 2.
    Hering C, Mai J-F (2012) Moment-based estimation of extendible Marshall-Olkin copulas. Metrika 75:601–620MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Loève M (1963) Probability theory. The university series in higher mathematics. Van Nostrand, Princeton NJzbMATHGoogle Scholar
  4. 4.
    Mai J-F (2014) Multivariate exponential distributions with latent factor structure and related topics. Habilitation thesis, Technische Universität München, MünchenGoogle Scholar
  5. 5.
    Mai J-F, Scherer M (2009) Lévy-frailty copulas. J Multivar Anal 100:1567–1585MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Mai J-F, Scherer M (2014) Financial engineering with copulas explained. Palgrave Macmillan, BasingstokCrossRefGoogle Scholar
  7. 7.
    Marshall AW, Olkin I (1967) A multivariate exponential distribution. J Am Stat Assoc 31:30–44MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Janina Engel
    • 1
  • Matthias Scherer
    • 1
    Email author
  • Leonhard Spiegelberg
    • 1
  1. 1.Technische Universität MünchenGarching-HochbrückGermany

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