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PRESERVATION OF PROPERTIES UNDER MIXTURE

Published online by Cambridge University Press:  27 February 2003

Henry W. Block ,
Yulin Li  and
Thomas H. Savits
Henry W. Block
Affiliation:
Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, E-mail: hwb@stat.pitt.edu
Yulin Li
Affiliation:
Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, E-mail: yulst12@stat.pitt.edu
Thomas H. Savits
Affiliation:
Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, E-mail: tsavits@stat.pitt.edu
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Abstract

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In general, finite mixtures of distributions with increasing failure rates are not increasing. However, conditions have been given by Lynch [8] so that a mixture of distributions with increasing failure rates has increasing failure rate. We establish similar results for other standard classes and also give examples which show that although the assumptions are stringent, continuous mixtures of standard families of lifetime distributions do have increasing failure rates. We also show that the result of Lynch follows from Savits [12] and the techniques of the last-cited paper can be applied to other classes as well.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 17 , Issue 2 , April 2003 , pp. 205 - 212
Copyright
© 2003 Cambridge University Press