Abstract
It is well known that mixtures of decreasing failure rate (DFR) distributions are always DFR. It turns out that, very often, mixtures of increasing failure rate (IFR) distributions can decrease at least in some intervals of time. Usually, this property can be observed asymptotically as t → ∞. In this article, several types of underlying continuous IFR distribution are considered. Two models of mixing are studied: additive and multiplicative. The limiting behavior of a mixture failure rate function is analyzed. It is shown that the conditional characteristics (expectation and variance) of the mixing parameter are crucial for the limiting behavior. Several examples are presented and possible generalizations are discussed.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Probability in the Engineering and Informational Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
