Univariate Ordering

  • R. Szekli
Part of the Lecture Notes in Statistics book series (LNS, volume 97)


Mathematical modeling in engineering and other fields which use as a tool the theory of probability involve concepts of comparison of random variables. The usual concept of partial order is applied to random variables random vectors, counting processes etc. Random behavior of variables is described mathematically for example by cumulative distribution functions, densities, Laplace transforms, moment generating functions, hazard rates or other functionals. Therefore we may apply the partial order concept to each of the equivalent descriptions of random variables. (For definitions see Appendix)


Service Time Busy Period UNIVARIATE Order Interarrival Time Nonnegative Random Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    This part of the proof can be passed by in the first readingGoogle Scholar
  2. 2.
    This part of the proof can be omitted in the first readingGoogle Scholar
  3. 3.
    The proof requires some knowledge about stopping times and conditioning, see Chapter 2 for needed definitionsGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • R. Szekli
    • 1
  1. 1.Mathematical InstituteUniversity of WroclawWroclawPoland

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