IDEAS home Printed from https://ideas.repec.org/p/iik/wpaper/162.html
   My bibliography  Save this paper

Stochastic Comparisons of Parallel Systems of Heterogeneous Generalized Exponential Components

Author

Listed:
  • Amarjit Kundu

    (Santipur College)

  • Shovan Chowdhury

    (Indian Institute of Management Kozhikode)

  • Asok K Nanda

    (Indian Institute of Science and Educational Research)

Abstract

Let X1, X2, . . . , Xn (resp. Y1, Y2, . . . , Yn) be independent random variables such that Xi (resp. Yi) follows generalized exponential distribution with shape parameter ?i and scale parameter ?i (resp. ?i), i = 1, 2, . . . , n. Here it is shown that if ? = (?1, ?2, . . . , ?n) majorizes ? = (?1, ?2, . . . , ?n) then Xn:n will be greater than Yn:n in reversed hazard rate ordering. That no relation exists between Xn:n and Yn:n, under same condition, in terms of likelihood ratio ordering has also been shown. It is also shown that, if Yi follows generalized exponential distribution with parameters ?, ?i , where ? is the mean of all ?i ’s, i = 1 . . . n, then Xn:n is greater than Yn:n in likelihood ratio ordering. In this context, an error in Marshall, Olkin and Arnold [Inequalities: Theory of Majorization and Its applications(2011)] has been corrected, and some new results on majorization have been developed.

Suggested Citation

  • Amarjit Kundu & Shovan Chowdhury & Asok K Nanda, 2014. "Stochastic Comparisons of Parallel Systems of Heterogeneous Generalized Exponential Components," Working papers 162, Indian Institute of Management Kozhikode.
    • Handle: RePEc:iik:wpaper:162
    as

    Download full text from publisher

    File URL: https://iimk.ac.in/websiteadmin/FacultyPublications/Working%20Papers/162abs.pdf?t=45
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhao, Peng & Li, Xiaohu & Balakrishnan, N., 2009. "Likelihood ratio order of the second order statistic from independent heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 952-962, May.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Peng Zhao & N. Balakrishnan, 2011. "Dispersive ordering of fail-safe systems with heterogeneous exponential components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 203-210, September.
    3. Peng Zhao & Yiying Zhang, 2014. "On the maxima of heterogeneous gamma variables with different shape and scale parameters," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(6), pages 811-836, August.
    4. Zhao, Peng & Balakrishnan, N., 2009. "Likelihood ratio ordering of convolutions of heterogeneous exponential and geometric random variables," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1717-1723, August.
    5. Peng Zhao & Feng Su, 2014. "On maximum order statistics from heterogeneous geometric variables," Annals of Operations Research, Springer, vol. 212(1), pages 215-223, January.
    6. Paltanea, Eugen, 2011. "Bounds for mixtures of order statistics from exponentials and applications," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 896-907, May.
    7. Wang, Jiantian, 2015. "A stochastic comparison result about hazard rate ordering of two parallel systems comprising of geometric components," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 86-90.
    8. Zhao, Peng, 2011. "Some new results on convolutions of heterogeneous gamma random variables," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 958-976, May.
    9. Balakrishnan, N. & Zhao, Peng, 2013. "Hazard rate comparison of parallel systems with heterogeneous gamma components," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 153-160.
    10. Ebrahim Amini-Seresht & Jianfei Qiao & Yiying Zhang & Peng Zhao, 2016. "On the skewness of order statistics in multiple-outlier PHR models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(7), pages 817-836, October.
    11. Ding, Weiyong & Zhang, Yiying & Zhao, Peng, 2013. "Comparisons of k-out-of-n systems with heterogenous components," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 493-502.
    12. Zhao, Peng & Balakrishnan, N., 2009. "Mean residual life order of convolutions of heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1792-1801, September.
    13. Bhattacharyya, Dhrubasish & Khan, Ruhul Ali & Mitra, Murari, 2020. "Stochastic comparisons of series, parallel and k-out-of-n systems with heterogeneous bathtub failure rate type components," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    14. Zhao, Peng & Balakrishnan, N., 2011. "New results on comparisons of parallel systems with heterogeneous gamma components," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 36-44, January.
    15. Zhao, Peng & Balakrishnan, N., 2010. "Ordering properties of convolutions of heterogeneous Erlang and Pascal random variables," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 969-974, June.
    16. Zhao, Peng & Balakrishnan, N., 2014. "A stochastic inequality for the largest order statistics from heterogeneous gamma variables," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 145-150.
    17. 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.
    18. Peng Zhao & N. Balakrishnan, 2015. "Comparisons of Largest Order Statistics from Multiple-outlier Gamma Models," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 617-645, September.
    19. 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.
    20. Ding, Weiyong & Da, Gaofeng & Zhao, Peng, 2013. "On sample ranges from two sets of heterogenous random variables," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 63-73.

    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:iik:wpaper:162. 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: Sudheesh Kumar (email available below). General contact details of provider: https://edirc.repec.org/data/iikmmin.html .

    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.