A sufficient condition of crossing type for the bivariate orthant convex order

Denuit, Michel;Mesfioui, Mhamed
(2013) Statistics & Probability Letters — Vol. 83, n° 1, p. 157-162 (2013)

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  • Denuit, MichelUCLouvain
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  • Mesfioui, MhamedUniversité du Québec, Trois Rivières
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Abstract
In this work, we derive a sufficient condition for the orthant convex order based on the single crossing of the respective joint survival functions. This condition is expressed in terms of the generators for Archimedean copulas. Numerical examples show that this condition is valid for members of standard copula families (including the Clayton and Frank ones).
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Denuit, M., & Mesfioui, M. (2013). A sufficient condition of crossing type for the bivariate orthant convex order. Statistics & Probability Letters, 83(1), 157-162. https://doi.org/10.1016/j.spl.2012.07.014 (Original work published 2013)