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Stochastic orderings of convolution residuals

Author

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  • Fariba Amiripour
  • Baha-Eldin Khaledi
  • Moshe Shaked

Abstract

In this paper we study convolution residuals, that is, if $$X_1,X_2,\ldots ,X_n$$ are independent random variables, we study the distributions, and the properties, of the sums $$\sum _{i=1}^lX_i-t$$ given that $$\sum _{i=1}^kX_i>t$$ , where $$t\in \mathbb R $$ , and $$1\le k\le l\le n$$ . Various stochastic orders, among convolution residuals based on observations from either one or two samples, are derived. As a consequence computable bounds on the survival functions and on the expected values of convolution residuals are obtained. Some applications in reliability theory and queueing theory are described. Copyright Springer-Verlag 2013

Suggested Citation

  • Fariba Amiripour & Baha-Eldin Khaledi & Moshe Shaked, 2013. "Stochastic orderings of convolution residuals," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 559-576, May.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:4:p:559-576
    DOI: 10.1007/s00184-012-0404-x
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    Cited by:

    1. Mansour Shrahili & Mohamed Kayid, 2023. "Stochastic Orderings of the Idle Time of Inactive Standby Systems," Mathematics, MDPI, vol. 11(20), pages 1-21, October.
    2. Mansour Shrahili & Mohamed Kayid, 2022. "Characterizations of the Exponential Distribution by Some Random Hazard Rate Sequences," Mathematics, MDPI, vol. 10(17), pages 1-11, August.
    3. Mohamed Kayid & Mashael A. Alshehri, 2023. "Stochastic Comparisons of Lifetimes of Used Standby Systems," Mathematics, MDPI, vol. 11(14), pages 1-17, July.

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