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Ordering extremes of exponentiated location-scale models with dependent and heterogeneous random samples

Author

Listed:
  • Sangita Das

    (National Institute of Technology Rourkela)

  • Suchandan Kayal

    (National Institute of Technology Rourkela)

Abstract

This paper is devoted to some ordering results for the largest and the smallest order statistics arising from dependent heterogeneous exponentiated location-scale random observations. We assume that the sets of observations are sharing a common or different Archimedean copula(s). Sufficient conditions for which the usual stochastic order and the reversed hazard rate order between the extreme order statistics hold are derived. Various numerical examples are provided for the illustration of the proposed results. Finally, some applications of the comparison results in engineering reliability and auction theory are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:8:d:10.1007_s00184-019-00753-2
    DOI: 10.1007/s00184-019-00753-2
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    References listed on IDEAS

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    1. Li, Chen & Li, Xiaohu, 2019. "Hazard rate and reversed hazard rate orders on extremes of heterogeneous and dependent random variables," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 104-111.
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    4. Narayanaswamy Balakrishnan & Phalguni Nanda & Suchandan Kayal, 2018. "Ordering of series and parallel systems comprising heterogeneous generalized modified Weibull components," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 34(6), pages 816-834, November.
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    7. Li, Xiaohu & Fang, Rui, 2015. "Ordering properties of order statistics from random variables of Archimedean copulas with applications," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 304-320.
    8. Chen Li & Rui Fang & Xiaohu Li, 2016. "Stochastic somparisons of order statistics from scaled and interdependent random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(5), pages 553-578, July.
    9. 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.
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    1. Vasile Preda & Luigi-Ionut Catana, 2021. "Tsallis Log-Scale-Location Models. Moments, Gini Index and Some Stochastic Orders," Mathematics, MDPI, vol. 9(11), pages 1-22, May.

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