MODELING A FAILURE RATE FOR A MIXTURE OF DISTRIBUTION FUNCTIONS
Max S. Finkelstein a1andVeronica Esaulova a2 a1 University of the Orange Free State,
9300 Bloemfontein, Republic of South Africa, E-mail:
MSF@wwg3.uovs.ac.za a2 Saint Petersburg State University, St.
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 [rightward arrow] [infty infinity]. 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.