Bartoszewicz and Benduch (2009) applied an idea of Lehmann and Rojo (1992) to a new setting and used the GTTT transform to define invariance properties and distances of some stochastic orders. In this paper Lehmann and Rojo's idea is applied to the class of models which is based on distributions which are compositions of distribution functions on [0,1] with underlying distributions. Some stochastic orders are invariant with respect to these models.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-3,
author = {Magdalena Fr\k aszczak and Jaros\l aw Bartoszewicz},
title = {Invariance of relative inverse function orderings under compositions of distributions},
journal = {Applicationes Mathematicae},
volume = {39},
year = {2012},
pages = {283-292},
zbl = {1261.60026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-3}
}
Magdalena Frąszczak; Jarosław Bartoszewicz. Invariance of relative inverse function orderings under compositions of distributions. Applicationes Mathematicae, Tome 39 (2012) pp. 283-292. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-3/