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ITERATED FAILURE RATE MONOTONICITY AND ORDERING RELATIONS WITHIN GAMMA AND WEIBULL DISTRIBUTIONS

Published online by Cambridge University Press:  24 January 2018

Idir Arab  and
Paulo Eduardo Oliveira Open the ORCID record for Paulo Eduardo Oliveira [Opens in a new window]
Idir Arab
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, Coimbra, Portugal E-mail:paulo@mat.uc.pt
Paulo Eduardo Oliveira
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, Coimbra, Portugal E-mail:paulo@mat.uc.pt
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Abstract

Stochastic ordering of random variables may be defined by the relative convexity of the tail functions. This has been extended to higher order stochastic orderings, by iteratively reassigning tail-weights. The actual verification of stochastic orderings is not simple, as this depends on inverting distribution functions for which there may be no explicit expression. The iterative definition of distributions, of course, contributes to make that verification even harder. We have a look at the stochastic ordering, introducing a method that allows for explicit usage, applying it to the Gamma and Weibull distributions, giving a complete description of the order of relations within each of these families.

Keywords

applied probabilitycomputational probabilitystochastic modelling
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 1 , January 2019 , pp. 64 - 80
Copyright
Copyright © Cambridge University Press 2018 

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