The results in Chapter 5 have many spin-off effects that concern the full class ℐ. These are the focus of this chapter. In Section 6.1 real characterizations of some transforms are given in terms of hyperbolic complete monotonicity (HCM) and then, in Section 6.2, the fruit of this work is harvested. It is shown that ℐ also has several multiplicative properties. Moreover, the effect of certain transformations of rv’s with distributions in ℐ is studied. In Section 6.3 essentially some large subclasses of ℐ are considered. A short summary of Chapters 5 and 6 is given in Section 6.4, and an attempt is made to widen the perspective.


Survival Function Scale Mixture Multiplicative Property Increase Failure Rate Nonnegative Measure 
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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Lennart Bondesson
    • 1
  1. 1.Department of Forest BiometrySwedish University of Agricultural SciencesUmeåSweden

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