Some Classes of Distributions Closed under the Formation of Coherent Systems
WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS
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It has been shown by Birnbaum, Esary and Marshall that the class of survival functions with increasing hazard rate average IHRA is closed under the formation of coherent systems. Moreover, this is the smallest class of survival functions which is closed both under the formation of coherent system and limits in distribution, and which contains the exponential survival functions. In this paper a number of other classes are found which are closed under the formation of coherent systems and limits in distribution. Associated subclasses that play a generating role like the exponential class in the IHRA case are exhibited. In addition, several methods are presented for deriving closed classes from closed classes.
- Statistics and Probability
- Manufacturing and Industrial Engineering and Control of Production Systems