Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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On the maximum and minimum in a bivariate uniform distribution

  • Lee, Changsoo (Department of Flight Operation, Kyungwoon University) ;
  • Shin, Hyejung (Department of Flight Operation, Kyungwoon University) ;
  • Moon, Yeung-Gil (Department of Tourism Quality Management, Kangwon Tourism College)
  • Received : 2015.05.19
  • Accepted : 2015.11.25
  • Published : 2015.11.30
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Abstract

We obtain means and variances of max {X, Y} and min {X, Y} in the underlying Morgenstern type bivariate uniform variables X and Y with same scale parameters and different scale parameters respectively. And we obtain the conditional expectations in the underlying Morgenstern type bivariate uniform variables. Here, we shall consider the conditional expectations to know the dependence of one variable on the other variable and we consider the behaviors of means and variances of max {X, Y} and min {X, Y} with respect to changes in means, variances, and the correlation coeffcient of the underlying Morgenstern type bivariate uniform variables.

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References

  1. Hakamipour, N., Mohammadpour, A. and Nadarajah, S. (2011). Extremes of a bivariate Pareto distribution. Information Technology and Control, 40, 83-87.
  2. Ker, A. P. (2001). On the maximum of bivariate normal random variables. Extremes, 4, 185-190. https://doi.org/10.1023/A:1013977210907
  3. Morgenstern, D. (1956). Einfache beispiele zweidimensionaler verteilungen. Mitteilungsblatt fur Mathematische Statistik . 8, 234-235.
  4. Lee, J. C. and Kang, J. H. (2014). Some properties of reliability, ratio, maximum and minimum in a bivariate exponential distribution with a dependence parameter. Journal of the Korean Data & Information Sciences Society, 25, 219-226. https://doi.org/10.7465/jkdi.2014.25.1.219
  5. Lien, D. (2005). On the minimum and maximum of bivariate lognormal random variables. Extremes, 8, 79-83. https://doi.org/10.1007/s10687-005-4861-8
  6. Tahmasebi, S. and Jafari, A. A. (2012). Estimation of a scale parameter of Morgenstern type bivariate uniform distribution by ranked set sampling. Journal of Data Science, 10, 129-141.
  7. Woo, J. and Nadarajah, S. (2013). On the maximum and minimum of multivariate Pareto random variables. Information Technology and Control, 42, 242-246.