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Switching Order Statistics through Random Power Contractions

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  • Jacek WesoŁowski
  • Mohammad Ahsanullah

Abstract

This paper investigates a new random contraction scheme which complements the length‐biasing and convolution contraction schemes considered in the literature. A random power contraction is used with order statistics, leading to new and elegant characterizations of the power distribution. In view of Rossberg's counter‐example of a non‐exponential law with exponentially distributed spacings of order statistics, possibly the most appealing consequence of the result is a characterization of the exponential distribution via an independent exponential shift of order statistics.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:anzsta:v:46:y:2004:i:2:p:297-303
    DOI: 10.1111/j.1467-842X.2004.00330.x
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    Cited by:

    1. 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.
    2. Shah, Imtiyaz A. & Khan, A.H. & Barakat, H.M., 2015. "Translation, contraction and dilation of dual generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 131-135.
    3. Ahsanullah Mohammad & Yanev George P. & Onica Constantin, 2012. "Characterizations of Logistic Distribution Through Order Statistics with Independent Exponential Shifts," Stochastics and Quality Control, De Gruyter, vol. 27(1), pages 85-96, September.
    4. Yanev, George P. & Chakraborty, Santanu, 2016. "A characterization of exponential distribution and the Sukhatme–Rényi decomposition of exponential maxima," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 94-102.
    5. 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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