Foschi, Rachele and Spizzichino, Fabio
Reversing conditional orderings.
Stochastic Orders in Reliability and Risk.
Lecture Notes in Statistics
Springer, pp. 59-80.
We analyze some specific aspects concerning conditional orderings and relations among them. To this purpose we define a suitable concept of reversed conditional ordering and prove some related results. In particular we aim to compare the univariate stochastic orderings ≤ st, ≤ hr, and ≤ lr in terms of differences among different notions of conditional orderings. Some applications of our result to the analysis of positive dependence will be detailed. We concentrate attention to the case of a pair of scalar random variables X, Y . Suitable extensions to multivariate cases are possible.
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