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The Mean of Marshall–Olkin-Dependent Exponential Random Variables

  • Lexuri FernándezEmail author
  • Jan-Frederik Mai
  • Matthias Scherer
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 141)

Abstract

The probability distribution of \(S_d:=X_1+\cdots +X_d\), where the vector \((X_1,\ldots ,X_d)\) is distributed according to the Marshall–Olkin law, is investigated. Closed-form solutions are derived in the general bivariate case and for \(d\in \{2,3,4\}\) in the exchangeable subfamily. Our computations can, in principle, be extended to higher dimensions, which, however, becomes cumbersome due to the large number of involved parameters. For the Marshall–Olkin distributions with conditionally independent and identically distributed components, however, the limiting distribution of \(S_d/d\) is identified as \(d\) tends to infinity. This result might serve as a convenient approximation in high-dimensional situations. Possible fields of application for the presented results are reliability theory, insurance, and credit-risk modeling.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Lexuri Fernández
    • 1
    Email author
  • Jan-Frederik Mai
    • 2
  • Matthias Scherer
    • 1
  1. 1.Lehrstuhl für Finanzmathematik (M13)Technische Universität MünchenGarching-HochbrückGermany
  2. 2.XAIA InvestmentMünchenGermany

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