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Journal of Probability and Statistics
Volume 2015, Article ID 159710, 6 pages
Research Article

Residual and Past Entropy for Concomitants of Ordered Random Variables of Morgenstern Family

1Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo 11884, Egypt
2Department of Mathematics and Statistics, Faculty of Science, Taif University, Hawia 888, Saudi Arabia
3Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11341, Egypt

Received 25 June 2015; Accepted 7 September 2015

Academic Editor: Chunsheng Ma

Copyright © 2015 M. M. Mohie EL-Din et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For a system, which is observed at time t, the residual and past entropies measure the uncertainty about the remaining and the past life of the distribution, respectively. In this paper, we have presented the residual and past entropy of Morgenstern family based on the concomitants of the different types of generalized order statistics (gos) and give the linear transformation of such model. Characterization results for these dynamic entropies for concomitants of ordered random variables have been considered.