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ON A CLASS OF GENERALIZED MARSHALL–OLKIN BIVARIATE DISTRIBUTIONS AND SOME RELIABILITY CHARACTERISTICS

Published online by Cambridge University Press:  28 March 2013

Ramesh C. Gupta,
S.N.U.A. Kirmani and
N. Balakrishnan
Ramesh C. Gupta
Affiliation:
Department of Mathematics and Statistics, University of Maine, Orono, ME 04469-5752
S.N.U.A. Kirmani
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614
N. Balakrishnan
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, CanadaL8S 4K1
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Abstract

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We consider here a general class of bivariate distributions from reliability point of view, and refer to it as generalized Marshall–Olkin bivariate distributions. This class includes as special cases the Marshall–Olkin bivariate exponential distribution and the class of bivariate distributions studied recently by Sarhan and Balakrishnan [25]. For this class, the reliability, survival, hazard, and mean residual life functions are all derived, and their monotonicity is discussed for the marginal as well as the conditional distributions. These functions are also studied for the series and parallel systems based on this bivariate distribution. Finally, the Clayton association measure for this bivariate model is derived in terms of the hazard gradient.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 2 , April 2013, pp. 261 - 275
Copyright
Copyright © Cambridge University Press 2013

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