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Limiting Distributions for the Minimum-Maximum Models

Author

Listed:
  • Ling Peng

    (School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China)

  • Lei Gao

    (School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China)

Abstract

We consider the extreme value problem of the minimum-maximum models for the independent and identically distributed random sequence and stationary random sequence, respectively. By invoking some probability formulas and Taylor’s expansions of the distribution functions, the limiting distributions for these two kinds of sequences are obtained. Moreover, convergence analysis is carried out for those extreme value distributions. Several numerical experiments are conducted to validate our theoretical results.

Suggested Citation

  • Ling Peng & Lei Gao, 2019. "Limiting Distributions for the Minimum-Maximum Models," Mathematics, MDPI, vol. 7(8), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:719-:d:255637
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    References listed on IDEAS

    as
    1. W. J. Hall & Jon A. Wellner, 1979. "The rate of convergence in law of the maximum of an exponential sample," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 33(3), pages 151-154, September.
    2. Laurens de Haan, 1976. "Sample extremes: an elementary introduction," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 30(4), pages 161-172, December.
    3. de Haan, Laurens, 1976. "Sample Extremes: An Elementary Introduction," Econometric Institute Archives 272130, Erasmus University Rotterdam.
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