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Some characterizations of distributions based on order statistics

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  • Papathanasiou, V.

Abstract

Let X(1), X(2) be the order statistics of a sample of size two from an absolutely continuous random variable X. We obtain upper bounds for the covariance of X(1), X(2), which can be used to derive characterizations for specific distributions. A bound for the variance of the ith order statistic X(i) from a sample of size n is also obtained.

Suggested Citation

  • Papathanasiou, V., 1990. "Some characterizations of distributions based on order statistics," Statistics & Probability Letters, Elsevier, vol. 9(2), pages 145-147, February.
    • Handle: RePEc:eee:stapro:v:9:y:1990:i:2:p:145-147
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    Cited by:

    1. Rychlik, Tomasz, 2008. "Extreme variances of order statistics in dependent samples," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1577-1582, September.
    2. Marek Beśka & Krzysztof Jasiński & Tomasz Rychlik & Marcin Spryszyński, 2012. "Mixed systems with minimal and maximal lifetime variances," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 877-894, October.
    3. Navarro, Jorge & Balakrishnan, N., 2010. "Study of some measures of dependence between order statistics and systems," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 52-67, January.
    4. Papadatos, N. & Papathanasiou, V., 1996. "A generalization of variance bounds," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 191-194, June.
    5. Balakrishnan, N. & Cramer, E. & Kamps, U., 2001. "Bounds for means and variances of progressive type II censored order statistics," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 301-315, October.

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