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Conditions for finiteness and bounds on moments of generalized order statistics

Author

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  • Mariusz Bieniek

    (University of Maria Curie-Skłodowska)

  • Tomasz Rychlik

    (Polish Academy of Sciences)

Abstract

We present necessary and sufficient conditions for the finiteness of moments of a fixed order of generalized order statistics based on an arbitrary life baseline distribution with a finite expectation. The conditions depend on a relation between the moment order and the minimal parameter of the generalized order statistic and its multiplicity. Furthermore, under these conditions we determine sharp upper bounds on the moments of generalized order statistic expressed in the scale units being the respective powers of the mean of the baseline distribution.

Suggested Citation

  • Mariusz Bieniek & Tomasz Rychlik, 2024. "Conditions for finiteness and bounds on moments of generalized order statistics," Statistical Papers, Springer, vol. 65(4), pages 2289-2312, June.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:4:d:10.1007_s00362-023-01482-5
    DOI: 10.1007/s00362-023-01482-5
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    References listed on IDEAS

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    1. Erhard Cramer & Udo Kamps, 2003. "Marginal distributions of sequential and generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 293-310, December.
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    6. Tomasz Rychlik, 2010. "Evaluations of generalized order statistics from bounded populations," Statistical Papers, Springer, vol. 51(1), pages 165-177, January.
    7. H. M. Barakat & E. M. Nigm & Magdy E. El-Adll & M. Yusuf, 2018. "Prediction of future generalized order statistics based on exponential distribution with random sample size," Statistical Papers, Springer, vol. 59(2), pages 605-631, June.
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