Title: Iterated failure rate monotonicity and ordering relations within Gamma and Weibull distributions,
Abstract: Stochastic ordering of distributions 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 those 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 relations
within each of those families.