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Extreme shock models: An alternative perspective

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  • Cirillo, Pasquale
  • Hüsler, Jürg

Abstract

Extreme shock models have been introduced in Gut and Hüsler (1999) to study systems that at random times are subject to a shock of random magnitude. These systems break down when the shock overcomes a given resistance level. In this paper we propose an alternative approach to extreme shock models using reinforced urn processes. As a consequence of this we are able to look at the same problem under a Bayesian nonparametric perspective, providing the predictive distribution of systems' defaults.

Suggested Citation

  • Cirillo, Pasquale & Hüsler, Jürg, 2011. "Extreme shock models: An alternative perspective," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 25-30, January.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:1:p:25-30
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    References listed on IDEAS

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    1. Cirillo, Pasquale & Hüsler, Jürg, 2009. "An urn approach to generalized extreme shock models," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 969-976, April.
    2. Muliere, Pietro & Secchi, Piercesare & G. Walker, Stephen, 2003. "Reinforced random processes in continuous time," Stochastic Processes and their Applications, Elsevier, vol. 104(1), pages 117-130, March.
    3. Muliere, P. & Secchi, P. & Walker, S. G., 2000. "Urn schemes and reinforced random walks," Stochastic Processes and their Applications, Elsevier, vol. 88(1), pages 59-78, July.
    4. Gut, Allan & Hüsler, Jürg, 2005. "Realistic variation of shock models," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 187-204, September.
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    Cited by:

    1. Eryilmaz, Serkan & Kan, Cihangir, 2019. "Reliability and optimal replacement policy for an extreme shock model with a change point," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    2. repec:bpj:demode:v:6:y:2018:i:1:p:131-138:n:8 is not listed on IDEAS
    3. Wang, Xiaoyue & Zhao, Xian & Wang, Siqi & Sun, Leping, 2020. "Reliability and maintenance for performance-balanced systems operating in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    4. Yang, Shunkun & Shao, Qi & Bian, Chong, 2022. "Reliability analysis of ensemble fault tolerance for soft error mitigation against complex radiation effect," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    5. Meango, Toualith Jean-Marc & Ouali, Mohamed-Salah, 2020. "Failure interaction model based on extreme shock and Markov processes," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    6. Fierro, Raúl & Leiva, Víctor & Maidana, Jean Paul, 2018. "Cumulative damage and times of occurrence for a multicomponent system: A discrete time approach," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 323-333.
    7. Zhao, Xian & Wang, Siqi & Wang, Xiaoyue & Cai, Kui, 2018. "A multi-state shock model with mutative failure patterns," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 1-11.
    8. Eryilmaz, Serkan, 2015. "Assessment of a multi-state system under a shock model," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 1-8.
    9. Peluso, Stefano & Mira, Antonietta & Muliere, Pietro, 2015. "Reinforced urn processes for credit risk models," Journal of Econometrics, Elsevier, vol. 184(1), pages 1-12.

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