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On a class exhibiting trend change in average failure rate

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  • Priyanka Majumder
  • Murari Mitra

Abstract

Weak convergence and moment convergence issues are investigated for the New Better than Average Failure Rate (NBAFR) family (introduced by Loh (1984)). We explore the validity of these results in the context of a more general ageing class that we introduce. We prove some new properties of this class and derive its interrelationships with other non-monotonic ageing families. Reliability and moment bounds are obtained and an interesting characterization of exponentiality is proved. Special cases of our results lead to new theorems for the NBAFR class. Finally weak convergence and related issues are established for this class.

Suggested Citation

  • Priyanka Majumder & Murari Mitra, 2020. "On a class exhibiting trend change in average failure rate," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(8), pages 1975-1988, April.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:8:p:1975-1988
    DOI: 10.1080/03610926.2019.1568479
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