IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v146y2019icp104-111.html
   My bibliography  Save this article

Hazard rate and reversed hazard rate orders on extremes of heterogeneous and dependent random variables

Author

Listed:
  • Li, Chen
  • Li, Xiaohu

Abstract

We develop sufficient conditions for the hazard rate order on minimums of sample with Archimedean survival copulas and having proportional hazard rates or scales, and the reversed hazard rate order on maximums of sample with Archimedean copulas and have proportional reversed hazard rates, respectively. Also, we present applications of the hazard rate order on sample minimums in engineering reliability and actuarial risk.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:146:y:2019:i:c:p:104-111
    DOI: 10.1016/j.spl.2018.11.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715218303523
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2018.11.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chen Li & Xiaohu Li, 2017. "Aging and ordering properties of multivariate lifetimes with Archimedean dependence structures," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(2), pages 874-891, January.
    2. 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.
    3. Nil Kamal Hazra & Mithu Rani Kuiti & Maxim Finkelstein & Asok K. Nanda, 2018. "On stochastic comparisons of minimum order statistics from the location–scale family of distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(2), pages 105-123, February.
    4. Rezapour, Mohsen & Alamatsaz, Mohammad Hossein, 2014. "Stochastic comparison of lifetimes of two (n−k+1)-out-of-n systems with heterogeneous dependent components," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 240-251.
    5. Hazra, Nil Kamal & Kuiti, Mithu Rani & Finkelstein, Maxim & Nanda, Asok K., 2017. "On stochastic comparisons of maximum order statistics from the location-scale family of distributions," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 31-41.
    6. Li, Xiaohu & Da, Gaofeng & Zhao, Peng, 2010. "On reversed hazard rate in general mixture models," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 654-661, April.
    7. 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.
    8. Li, Chen & Li, Xiaohu, 2015. "Likelihood ratio order of sample minimum from heterogeneous Weibull random variables," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 46-53.
    9. Fang, Rui & Li, Xiaohu, 2015. "Advertising a second-price auction," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 246-252.
    10. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Junrui Wang & Rongfang Yan & Bin Lu, 2020. "Stochastic Comparisons of Parallel and Series Systems with Type II Half Logistic-Resilience Scale Components," Mathematics, MDPI, vol. 8(4), pages 1-18, March.
    2. 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.
    3. 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.
    4. Barmalzan, Ghobad & Akrami, Abbas & Balakrishnan, Narayanaswamy, 2020. "Stochastic comparisons of the smallest and largest claim amounts with location-scale claim severities," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 341-352.
    5. Mesfioui Mhamed & Trufin Julien, 2021. "Dispersive order comparisons on extreme order statistics from homogeneous dependent random vectors," Dependence Modeling, De Gruyter, vol. 9(1), pages 385-393, January.
    6. Ariyafar, Saeed & Tata, Mahbanoo & Rezapour, Mohsen & Madadi, Mohsen, 2020. "Comparison of aggregation, minimum and maximum of two risky portfolios with dependent claims," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    7. Sangita Das & Suchandan Kayal & N. Balakrishnan, 2021. "Orderings of the Smallest Claim Amounts from Exponentiated Location-Scale Models," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 971-999, September.
    8. Nil Kamal Hazra & Mithu Rani Kuiti & Maxim Finkelstein & Asok K. Nanda, 2018. "On stochastic comparisons of minimum order statistics from the location–scale family of distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(2), pages 105-123, February.
    9. Chen Li & Xiaohu Li, 2020. "Weak aging properties for coherent systems with statistically dependent component lifetimes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 559-572, October.
    10. M. Mesfioui & M. Kayid & S. Izadkhah, 2017. "Stochastic comparisons of order statistics from heterogeneous random variables with Archimedean copula," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 749-766, November.
    11. Khan, Ruhul Ali, 2023. "Two-sample nonparametric test for proportional reversed hazards," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    12. Zhengcheng Zhang & N. Balakrishnan, 2016. "Representations of the inactivity time for coherent systems with heterogeneous components and some ordered properties," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 113-126, January.
    13. Jørgen Vitting Andersen & Roy Cerqueti & Giulia Rotundo, 2017. "Rational expectations and stochastic systems," Documents de travail du Centre d'Economie de la Sorbonne 17060, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2019.
    14. Li, Chen & Li, Xiaohu, 2015. "Likelihood ratio order of sample minimum from heterogeneous Weibull random variables," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 46-53.
    15. Longxiang Fang & Narayanaswamy Balakrishnan & Wenyu Huang & Shuai Zhang, 2023. "Usual stochastic ordering of the sample maxima from dependent distribution‐free random variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(1), pages 99-112, February.
    16. Eryilmaz, Serkan & Ozkut, Murat, 2020. "Optimization problems for a parallel system with multiple types of dependent components," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    17. M. Salehi & Z. Shishebor & M. Asadi, 2019. "On the reliability modeling of weighted k-out-of-n systems with randomly chosen components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(5), pages 589-605, July.
    18. Belzunce, Félix & Suárez-Llorens, Alfonso & Sordo, Miguel A., 2012. "Comparison of increasing directionally convex transformations of random vectors with a common copula," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 385-390.
    19. Enrique de Amo & María del Rosario Rodríguez-Griñolo & Manuel Úbeda-Flores, 2024. "Directional Dependence Orders of Random Vectors," Mathematics, MDPI, vol. 12(3), pages 1-14, January.
    20. Tazi, Nacef & Châtelet, Eric & Bouzidi, Youcef, 2018. "How combined performance and propagation of failure dependencies affect the reliability of a MSS," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 531-541.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:146:y:2019:i:c:p:104-111. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.