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On stochastic comparisons of minimum order statistics from the location–scale family of distributions

Author

Listed:
  • Nil Kamal Hazra

    (University of the Free State)

  • Mithu Rani Kuiti

    (Indian Institute of Management Calcutta (IIMC))

  • Maxim Finkelstein

    (University of the Free State
    ITMO University)

  • Asok K. Nanda

    (Indian Institute of Science Education and Research (IISER) Kolkata)

Abstract

We consider stochastic comparisons of minimum order statistics from the location–scale family of distributions that contain most of the popular lifetime distributions. Under certain assumptions, we show that the minimum order statistic of one set of random variables dominates that of another set of random variables with respect to different stochastic orders. Furthermore, we illustrate our results using some well-known specific distributions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:2:d:10.1007_s00184-017-0636-x
    DOI: 10.1007/s00184-017-0636-x
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Weiyong Ding & Jiaxin Yang & Xiaoliang Ling, 2017. "On the skewness of extreme order statistics from heterogeneous samples," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(5), pages 2315-2331, March.
    4. 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.
    5. Proschan, F. & Sethuraman, J., 1976. "Stochastic comparisons of order statistics from heterogeneous populations, with applications in reliability," Journal of Multivariate Analysis, Elsevier, vol. 6(4), pages 608-616, December.
    6. Subhash C. Kochar & Nuria Torrado, 2015. "On Stochastic Comparisons of Largest Order Statistics in the Scale Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(19), pages 4132-4143, October.
    7. 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.
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    Cited by:

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    2. 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.
    3. 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.
    4. 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.

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