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Some new results involving the NBU(2) class of life distributions

Part of: Distribution theory Special processes

Published online by Cambridge University Press:  14 July 2016

Xiaohu Li  and
Subhash C. Kochar
Xiaohu Li*
Affiliation:
Lanzhou University
Subhash C. Kochar*
Affiliation:
Indian Statistical Institute, Delhi
*
∗ Postal address: Department of Mathematics, Lanzhou University, Lanzhou 730000, Gansu Province, China. Email address: [email protected]
∗∗ Postal address: Statistics and Mathematics Unit, Indian Statistical Institute, 7, S.J.S. Sansanwal Marg, New Delhi 110016, India.
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Abstract

Some new results about the NBU(2) class of life distributions are obtained. Firstly, it is proved that the decreasing with time of the increasing concave ordering of the excess lifetime in a renewal process leads to the NBU(2) property of the interarrival times. Secondly, the NBU(2) class of life distributions is proved to be closed under the formation of series systems. Finally, it is also shown that the NBU(2) class is closed under convolution operation.

Keywords

convolutionexcess lifetimeNBU(2)series systems

MSC classification

Primary: 62E10: Characterization and structure theory
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 1 , March 2001 , pp. 242 - 247
Copyright
Copyright © by the Applied Probability Trust 2001 

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