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On stochastic comparisons of maximum order statistics from the location-scale family of distributions

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  • Hazra, Nil Kamal
  • Kuiti, Mithu Rani
  • Finkelstein, Maxim
  • Nanda, Asok K.

Abstract

We consider the location-scale family of distributions, which contains many standard lifetime distributions. We give conditions under which the largest order statistic of a set of random variables with different/the same location as well as different/the same scale parameters dominates that of another set of random variables with respect to various stochastic orders. Along with general results, we consider important special cases, namely, the Feller–Pareto, generalized Pareto, Burr, exponentiated Weibull, Power generalized Weibull, generalized gamma, Half-normal and Fréchet distributions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:160:y:2017:i:c:p:31-41
    DOI: 10.1016/j.jmva.2017.06.001
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    References listed on IDEAS

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    1. Paulo Oliveira & Nuria Torrado, 2015. "On proportional reversed failure rate class," Statistical Papers, Springer, vol. 56(4), pages 999-1013, November.
    2. 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.
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    6. 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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    9. 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.
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    Cited by:

    1. 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.
    2. Sangita Das & Suchandan Kayal, 2021. "Ordering results between the largest claims arising from two general heterogeneous portfolios," Papers 2104.08605, arXiv.org.
    3. Ernesto-Jesús Veres-Ferrer & Jose M. Pavía, 2022. "The Elasticity of a Random Variable as a Tool for Measuring and Assessing Risks," Risks, MDPI, vol. 10(3), pages 1-38, March.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Nil Kamal Hazra & Maxim Finkelstein, 2018. "On stochastic comparisons of finite mixtures for some semiparametric families of distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 988-1006, December.
    10. 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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