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Exponential characterizations motivated by the structure of order statistics in samples of size two


  • Arnold, Barry C.
  • Villasenor, Jose A.


Motivated by the observation that for a sample of size two from an exponential distribution, the largest order statistic is distributed as a convolution of two independent exponential random variables with distributions differing only in their intensity or rate parameter, a spectrum of related characterizations of the exponential distribution are identified and verified.

Suggested Citation

  • Arnold, Barry C. & Villasenor, Jose A., 2013. "Exponential characterizations motivated by the structure of order statistics in samples of size two," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 596-601.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:596-601
    DOI: 10.1016/j.spl.2012.10.028

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    Cited by:

    1. Jovanović, Milan & Milošević, Bojana & Nikitin, Ya. Yu. & Obradović, Marko & Volkova, K. Yu., 2015. "Tests of exponentiality based on Arnold–Villasenor characterization and their efficiencies," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 100-113.
    2. Kayid, M. & Izadkhah, S., 2015. "Characterizations of the exponential distribution by the concept of residual life at random time," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 164-169.
    3. 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.


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