Comparisons of Parallel Systems According to the Convex Transform Order

By Subhash C. Kochar, Maochao Xu. Journal of Applied Probability, 2009

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ORDERING PROPERTIES OF ORDER STATISTICS FROM HETEROGENEOUS POPULATIONS: A REVIEW WITH AN EMPHASIS ON SOME RECENT DEVELOPMENTS (2013, background): “Kochar and Xu [31] proved that the largest order statistic from heterogeneous exponential variables is more skewed in the sense of convex transform order than that from homogeneous exponential variables, which is quite a general result as there is no any restriction on the parameters.”
On the skewness of order statistics in multiple-outlier models (2011, methodology): “…the ordering of the expectations of the random variables under the given conditions. https://doi.org/10.1239/jap/1300198149 Published online by Cambridge University Press Using arguments similar to those in Theorem 4.5 of Kochar and Xu (2009), we can extend the above result to the PHR models.”
Stochastic comparisons on sample extremes of dependent and heterogenous observations (2016, unknown): “See, for example, Kochar and Xu.[29,30] Note that λ ≤ (≥)λ̄ is equivalent to λ1 w ( w)λ and there is no implication between an increasing x[− ln(− ln F̄(x))]′ and F with DFR.”