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Switching record and order statistics via random contractions

Author

Listed:
  • Oncel, Sevgi Yurt
  • Ahsanullah, Mohammad
  • Aliev, Fazil A.
  • Aygun, Funda

Abstract

In this paper, we investigate a random contraction scheme proposed by Wesolowski and Ahsanullah (2004. Austral. NZ J. Statist. 46, 297-303). Random contraction is used in the record and order statistics settings. Some distributional recurrence relations were found for the probability density functions and distribution functions of record and order statistics. These recurrence relations lead to new characterizations of some distributions. Our results are extensions of works by Pakes (1992. Austral. J. Statist. 34, 323-339), Wesolowski and Ahsanullah (2004. Austral. NZ J. Statist. 46, 297-303) and Alzaid and Ahsanullah (2003. Comm. Statist. Theory Methods 32, 2101-2108). Some new characterizations for the Weibull and Pareto distributions and one special distribution are provided in this study.

Suggested Citation

  • Oncel, Sevgi Yurt & Ahsanullah, Mohammad & Aliev, Fazil A. & Aygun, Funda, 2005. "Switching record and order statistics via random contractions," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 207-217, July.
    • Handle: RePEc:eee:stapro:v:73:y:2005:i:3:p:207-217
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    References listed on IDEAS

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    1. Anthony Pakes, 1994. "Necessary conditions for characterization of laws via mixed sums," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 797-802, December.
    2. Jacek WesoŁowski & Mohammad Ahsanullah, 2004. "Switching Order Statistics through Random Power Contractions," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 46(2), pages 297-303, June.
    3. Kotz, S. & Steutel, F. W., 1988. "Note on a characterization of exponential distributions," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 201-203, February.
    4. Yeo, G. F. & Milne, R. K., 1991. "On characterizations of beta and gamma distributions," Statistics & Probability Letters, Elsevier, vol. 11(3), pages 239-242, March.
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    Cited by:

    1. Shah, Imtiyaz A. & Barakat, H.M. & Khan, A.H., 2020. "Characterizations through generalized and dual generalized order statistics, with an application to statistical prediction problem," Statistics & Probability Letters, Elsevier, vol. 163(C).

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