Understanding the shape of the mixture failure rate (with engineering and demographic applications)
AbstractMixtures of distributions are usually effectively used for modeling heterogeneity. It is well known that mixtures of DFR distributions are always DFR. On the other hand, mixtures of IFR distributions can decrease, at least in some intervals of time. As IFR distributions often model lifetimes governed by ageing processes, the operation of mixing can dramatically change the pattern of ageing. Therefore, the study of the shape of the observed (mixture) failure rate in a heterogeneous setting is important in many applications. We study discrete and continuous mixtures, obtain conditions for the mixture failure rate to tend to the failure rate of the strongest populations and describe asymptotic behavior as t tends to infty. Some demographic and engineering examples are considered. The corresponding inverse problem is discussed.
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Bibliographic InfoPaper provided by Max Planck Institute for Demographic Research, Rostock, Germany in its series MPIDR Working Papers with number WP-2009-031.
Length: 24 pages
Date of creation: Nov 2009
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Web page: http://www.demogr.mpg.de/
Find related papers by JEL classification:
- J1 - Labor and Demographic Economics - - Demographic Economics
- Z0 - Other Special Topics - - General
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