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ON CONDITIONS FOR MIXTURES OF INCREASING FAILURE RATE DISTRIBUTIONS TO HAVE AN INCREASING FAILURE RATE

Published online by Cambridge University Press:  01 January 1999

James D. Lynch
James D. Lynch
Affiliation:
Department of Statistics, University of South Carolina, Columbia, South Carolina 29208
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Abstract

Consider a family of distributions with survival distributions that are log concave and stochastically increasing in a parameter over which it will be mixed. It is shown that a necessary and sufficient condition for a mixture over any such family to have an increasing failure rate is that the mixing distribution have an increasing failure rate. Some observations are given on generalizing this result as well as weakening the conditions on Prekopa's Theorem.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 13 , Issue 1 , January 1999 , pp. 33 - 36
Copyright
© 1999 Cambridge University Press

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