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Convergence in distribution of quotients of order statistics

Author

Listed:
  • Smid, B.
  • Stam, A. J.

Abstract

Let X1, X2,... be i.i.d. random variables with continuous distribution function F [infinity], with distribution functions xkp, K = 1, 2, .... A strong converse is proved, viz. convergence in distribution of this type of one of the quotients implies regular varation of 1 - F(x).

Suggested Citation

  • Smid, B. & Stam, A. J., 1975. "Convergence in distribution of quotients of order statistics," Stochastic Processes and their Applications, Elsevier, vol. 3(3), pages 287-292, July.
    • Handle: RePEc:eee:spapps:v:3:y:1975:i:3:p:287-292
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    Cited by:

    1. Cooke, Roger M. & Nieboer, Daan, 2011. "Heavy-Tailed Distributions: Data, Diagnostics, and New Developments," RFF Working Paper Series dp-11-19, Resources for the Future.
    2. Sophie A. Ladoucette & Jef L. Teugels, 2007. "Asymptotics for Ratios with Applications to Reinsurance," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 225-242, June.
    3. Enkelejd Hashorva & Claudio Macci & Barbara Pacchiarotti, 2013. "Large Deviations for Proportions of Observations Which Fall in Random Sets Determined by Order Statistics," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 875-896, December.
    4. Ipsen, Yuguang & Maller, Ross & Resnick, Sidney, 2019. "Ratios of ordered points of point processes with regularly varying intensity measures," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 205-222.

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