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Research Articles

HR and RHR orderings of extremes of dependent variables under Archimedean copula

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Pages 4776-4789 | Received 31 May 2022, Accepted 02 Mar 2023, Published online: 23 Mar 2023

References

  • Balakrishnan, N., G. Barmalzan, and A. Haidari. 2018. Modified proportional hazard rates and proportional reversed hazard rates models via Marshall-Olkin distribution and some stochastic comparisons. Journal of the Korean Statistical Society 47:127–38.
  • Balakrishnan, N., and C. R. Rao. (Eds.). 1998a. Handbook of statistics-Vol.16: Order statistics: Theory and methods. Amsterdam: Elsevier.
  • Balakrishnan, N., and C. R. Rao. (Eds.), 1998b. Handbook of statistics-Vol.17: Order statistics: Applications. Amsterdam: Elsevier.
  • Barmalzan, G., N. Balakrishnan, S. M. Ayat, and A. Akrami. 2021. Orderings of extremes dependent modified proportional hazard and modified proportional reversed hazard variables under Archimedean copula. Communications in Statistics-Theory and Methods 50 (22):5358–79.
  • Barmalzan, G., N., Balakrishnan, S. M., Ayat and A. Akrami. 2022. Orderings of extremes dependent modified proportional hazard and modified proportional reversed hazard variables under Archimedean copula. Communications in Statistics-Theory and Methods (to appear).
  • David, H. A., and H. N. Nagaraja. 2003. Order statistics. 3rd ed. Hoboken, NJ: John Wiley & Sons.
  • Fang, R., and X. Li. 2018. Ordering extremes of interdependent random variables. Communications in Statistics-Theory and Methods 47:4187–201.
  • Fang, R., C. Li, and X. Li. 2016. Stochastic comparisons on sample extremes of dependent and heterogeneous observations. Statistics 50:930–55.
  • Kotz, S., N. Balakrishnan, and N. L. Johnson. 2000. Continuous multivariate distributions. Vol.1, 2nd ed. New York: John Wiley & Sons.
  • Li, X., and R. Fang. 2015. Ordering properties of order statistics from random variables of Archimedean copulas with applications. Journal of Multivariate Analysis 133:304–20.
  • Li, C., R. Fang, and X. Li. 2015. Stochastic comparisons of order statistics from scaled and interdependent random variables. Metrika 79:553–78.
  • Li, C., and X. Li. 2019. Hazard rate and reversed hazard rate orders on extremes of heterogeneous and dependent random variables. Statistics & Probability Letters 146:104–11.
  • Marshall, A. W., and I. Olkin. 1997. A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84:641–52.
  • Marshall, A. W., and I. Olkin. 2007. Life distributions. New York: Springer.
  • Marshall, A. W., I. Olkin, and B. C. Arnold. 2011. Inequalities: Theory of majorization and its applications. 2nd ed. New York: Springer.
  • McNeil, A. J., and J. Něslehová. 2009. Multivariate Archimedean copulas, D-monotone functions and l1-norm symmetric distributions. The Annals of Statistics, 37: 3059–97.
  • Müller, A., and D. Stoyan. 2002. Comparison methods for stochastic models and risks. New York: John Wiley & Sons.
  • Nelsen, R. B. 2006. An introduction to copulas. New York: Springer.
  • Rezapour, M., and M. H. Alamatsaz. 2014. Stochastic comparison of lifetimes of two (n−k+1)-out-of-n systems with heterogeneous dependent components. Journal of Multivariate Analysis, 130: 240–51.
  • Righter, R., M. Shaked, and J. G. Shanthikumar. 2009. Intrinsic aging and classes of nonparametric distributions. Probability in the Engineering and Informational Sciences 23:563–82.
  • Ristic, M. M., K. K. Jose, and J. Ancy. 2007. A Marshall-Olkin gamma distribution and minification process. STARS: Stress and Anxiety Research Society, 11:107–17.
  • Saunders, I. W., and P. A. Moran. 1978. On the quantiles of the gamma and F distributions.Journal of Applied Probability, 15 (2): 426–32.
  • Shaked, M., and J. G. Shanthikumar. 2007. Stochastic orders. New York: Springer.
  • van Zwet, W. R. 1964. Convex transformations of random variables. Amsterdam: Mathematisch Centrum,
  • Zhang, Y., X. Cai, P. Zhao, and H. H. Wang. 2018. Stochastic comparisons of parallel and series systems with heterogeneous resilience-scaled components. Statistics 5:126–47.

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