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A multivariate IFR class

Published online by Cambridge University Press:  14 July 2016

Thomas H. Savits
Thomas H. Savits*
Affiliation:
University of Pittsburgh
*
∗Postal address: Department of Mathematics and Statistics, University of Pittsburgh, PA 15260, USA.
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Abstract

A non-negative random vector T is said to have a multivariate increasing failure rate distribution (MIFR) if and only if E[h(x, T)] is log concave in x for all functions h(x, t) which are log concave in (x, t) and are non-decreasing and continuous in t for each fixed x. This class of distributions is closed under deletion, conjunction, convolution and weak limits. It contains the multivariate exponential distribution of Marshall and Olkin and those distributions having a log concave density. Also, it follows that if T is MIFR and ψ is non-decreasing, non-negative and concave then ψ (T) is IFR.

Keywords

LOG CONCAVEINEQUALITIES
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 1 , March 1985 , pp. 197 - 204
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Research supported by ONR Contract N00014–76–C–0839.

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