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PRESERVATION OF STOCHASTIC ORDERS UNDER MIXTURES OF EXPONENTIAL DISTRIBUTIONS

Published online by Cambridge University Press:  19 September 2006

Jarosław Bartoszewicz  and
Magdalena Skolimowska
Jarosław Bartoszewicz
Affiliation:
Mathematical Institute, University of Wrocław, 50-384 Wrocław, Poland, E-mail: jarbar@math.uni.wroc.pl; mskolim@math.uni.wroc.pl
Magdalena Skolimowska
Affiliation:
Mathematical Institute, University of Wrocław, 50-384 Wrocław, Poland, E-mail: jarbar@math.uni.wroc.pl; mskolim@math.uni.wroc.pl
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Abstract

Recently, Bartoszewicz [5,6] considered mixtures of exponential distributions treated as the Laplace transforms of mixing distributions and established some stochastic order relations between them: star order, dispersive order, dilation. In this article the preservation of the likelihood ratio, hazard rate, reversed hazard rate, mean residual life, and excess wealth orders under exponential mixtures is studied. Some new preservation results for the dispersive order are given, as well as the preservation of the convex transform order, and the star one is discussed.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 4 , October 2006 , pp. 655 - 666
Copyright
© 2006 Cambridge University Press

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