Local limit theorems for shock models

Edward Omey, Rein Vesilo

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In many physical systems, failure occurs when the stress after shock n first exceed a critical level x.We consider the number of shocks τ(x) to failure and obtain more detailed information that is usually obtained about asymptotic distribution by using local limit theorems. We consider extreme and cumulative shock models with both univariate and multivariate shock types. We derive the limiting distribution of τ(x) and the rate of convergence to that. For the extreme shock model, rate of convergence for regularly varying shock distributions is found using the weighted Kolmorogov probability metric. For the cumulative shock model, we examine the rate of convergence to Gaussian densities.

Original languageEnglish
Pages (from-to)221-247
Number of pages27
JournalBrazilian Journal of Probability and Statistics
Volume30
Issue number2
DOIs
Publication statusPublished - 1 May 2016

Keywords

  • Extreme value theory
  • Local limit theory
  • Regular variation
  • Renewal theory
  • Shock models

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