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On Life Distributions Having Monotone Residual Variance

Published online by Cambridge University Press:  27 July 2009

Ramesh C. Gupta ,
S. N. U. A. Kirmani  and
Robert L. Launer
Ramesh C. Gupta
Affiliation:
University of Maine Orono, Maine 04469
S. N. U. A. Kirmani
Affiliation:
University of Northern Iowa Cedar Falls, Iowa 50614
Robert L. Launer
Affiliation:
U.S. Army Research OfficeResearch Triangle ParkNorth Carolina 27709
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Abstract

Launer [6] introduced the class of life distributions having decreasing (increasing) variance residual life, DVRL (IVRL). It is shown that the DVRL (IVRL) distributions are intimately connected to the behavior of the mean residual life function of the equilibrium distribution. Some counter examples are presented to demonstrate the lack of relationship between DVRL (IVRL) and NBUE (new better than used in expectation) (NWUE; new worse than used in expectation) distributions. Finally, we obtain bounds on moments and survival functions of DVRL (IVRL) distributions. These bounds turn out to be improvements on the previously known bounds for decreasing (increasing) mean residual life (DMRL (IMRL)) distributions.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 1 , Issue 3 , July 1987 , pp. 299 - 307
Copyright
Copyright © Cambridge University Press 1987

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