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Comparisons Between Largest Order Statistics from Multiple-outlier Models with Dependence

Author

Listed:
  • Jorge Navarro

    (Universidad de Murcia)

  • Nuria Torrado

    (Universidad Autónoma de Madrid)

  • Yolanda del Águila

    (Universidad de Almería)

Abstract

We study stochastic comparisons between the largest order statistics from samples which may contain outliers. The data in each sample can also be dependent. Under these assumptions we study three cases. In the first one we consider the general case without additional assumptions. In the second we assume that the data come from two different distributions. In the third one we assume that the data come from a proportional hazard rates model. The results obtained here can be applied to compare parallel systems. Some illustrative examples are provided.

Suggested Citation

  • Jorge Navarro & Nuria Torrado & Yolanda del Águila, 2018. "Comparisons Between Largest Order Statistics from Multiple-outlier Models with Dependence," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 411-433, March.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:1:d:10.1007_s11009-017-9562-7
    DOI: 10.1007/s11009-017-9562-7
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    References listed on IDEAS

    as
    1. Navarro, Jorge & Rychlik, Tomasz, 2010. "Comparisons and bounds for expected lifetimes of reliability systems," European Journal of Operational Research, Elsevier, vol. 207(1), pages 309-317, November.
    2. Misra, Neeraj & Misra, Amit Kumar, 2012. "New results on stochastic comparisons of two-component series and parallel systems," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 283-290.
    3. Jorge Navarro & Fabio Spizzichino, 2010. "Comparisons of series and parallel systems with components sharing the same copula," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(6), pages 775-791, November.
    4. Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2004. "A new class of bivariate copulas," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 315-325, February.
    5. Jorge Navarro & M. Carmen Gomis, 2016. "Comparisons in the mean residual life order of coherent systems with identically distributed components," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(1), pages 33-47, January.
    6. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
    7. Navarro, Jorge & Pellerey, Franco & Di Crescenzo, Antonio, 2015. "Orderings of coherent systems with randomized dependent components," European Journal of Operational Research, Elsevier, vol. 240(1), pages 127-139.
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    Citations

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    Cited by:

    1. Torrado, Nuria, 2022. "Optimal component-type allocation and replacement time policies for parallel systems having multi-types dependent components," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    2. Antonio Di Crescenzo & Abdolsaeed Toomaj, 2022. "Weighted Mean Inactivity Time Function with Applications," Mathematics, MDPI, vol. 10(16), pages 1-30, August.
    3. Jorge Navarro & Franco Pellerey & Miguel A. Sordo, 2020. "Weak Dependence Notions and Their Mutual Relationships," Mathematics, MDPI, vol. 9(1), pages 1-27, December.
    4. Navarro, Jorge & Fernández-Martínez, Pedro, 2021. "Redundancy in systems with heterogeneous dependent components," European Journal of Operational Research, Elsevier, vol. 290(2), pages 766-778.
    5. Sangita Das & Suchandan Kayal, 2020. "Ordering extremes of exponentiated location-scale models with dependent and heterogeneous random samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(8), pages 869-893, November.
    6. Jorge Navarro, 2018. "Stochastic comparisons of coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(4), pages 465-482, May.
    7. Torrado, Nuria & Arriaza, Antonio & Navarro, Jorge, 2021. "A study on multi-level redundancy allocation in coherent systems formed by modules," Reliability Engineering and System Safety, Elsevier, vol. 213(C).

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