Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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CHARACTERIZATIONS OF PARETO, WEIBULL AND POWER FUNCTION DISTRIBUTIONS BASED ON GENERALIZED ORDER STATISTICS

  • Ahsanullah, Mohammad (Department of Management Sciences Rider University) ;
  • Hamedani, G.G. (Department of Mathematics, Statistics and Computer Science Marquette University)
  • Received : 2014.09.02
  • Accepted : 2016.07.15
  • Published : 2016.08.15
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Abstract

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterization of Pareto and Weibull distributions based on the conditional expectation of generalized order statistics extending the characterization results reported by Jin and Lee (2014). We also present a characterization of the power function distribution based on the conditional expectation of lower generalized order statistics.

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References

  1. M. Ahsanullah and G. G. Hamedani, Characterizations of continuous distributions based on conditional expectation of generalized order statistics, Comm. Statist. Theory-Methods 42 (2013), 3608-3613. https://doi.org/10.1080/03610926.2011.635255
  2. M. Ahsanullah and G. G. Hamedani, Exponential Distribution: Theory and Methods, NOVA Publishers, (2010).
  3. M. Bieniek, A note on characterizations of distributions by regressions of nonadjacent generalized order statistics, Aust. N. Z. J. Stat. 51 (2009), 89-99. https://doi.org/10.1111/j.1467-842X.2008.00530.x
  4. M. Bieniek and D. Szynal, Characterizations of distributions via linearity of regression of generalized order statistics, Metrika 58 (2003), 259-271. https://doi.org/10.1007/s001840300263
  5. M. Burkschat, H. Cramer, and U. Kamps, Dual Generalized Order Statistics, Metron, LXI, (2003), 13-26.
  6. E. Cramer, U. Kamps, and C. Keseling, Characterizations via linear regression of ordered random variables: a unifying approach, Comm. Statist. Theory-Methods 33 (2004), 2885-2911. https://doi.org/10.1081/STA-200038832
  7. H-W. Jin and M-Y. Lee, On characterizations of Pareto and Weibull distribution by considering conditional expectations of upper record values, J. of Chungcheong Math. Sci. 27 (2014), no. 2, 243-247. https://doi.org/10.14403/jcms.2014.27.2.243
  8. U. Kamps, A concept of generalized order statistics, Teubner Skripten zur Mathematischen Stochastik. [Teubner Texts on Mathematical Stochastics]. B.G. Teubner, Stuttgart, (1995).