Multivariate Higher-Degree Stochastic Increasing Convexity

Michel M. Denuit () and Mhamed Mesfioui
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Michel M. Denuit: Université Catholique de Louvain
Mhamed Mesfioui: Université du Québec à Trois-Rivières

Journal of Theoretical Probability, 2016, vol. 29, issue 4, 1599-1623

Abstract: Abstract Building on the seminal work by Shaked and Shanthikumar (Adv Appl Probab 20:427–446, 1988a; Stoch Process Appl 27:1–20, 1988b), Denuit et al. (Eng Inf Sci 13:275–291, 1999; Methodol Comput Appl Probab 2:231–254, 2000; 2001) studied the stochastic s-increasing convexity properties of standard parametric families of distributions. However, the analysis is restricted there to a single parameter. As many standard families of distributions involve several parameters, multivariate higher-order stochastic convexity properties also deserve consideration for applications. This is precisely the topic of the present paper, devoted to stochastic $$(s_1,s_2,\ldots ,s_d)$$ ( s 1 , s 2 , … , s d ) -increasing convexity of distribution families indexed by a vector $$(\theta _1,\theta _2,\ldots ,\theta _d)$$ ( θ 1 , θ 2 , … , θ d ) of parameters. This approach accounts for possible correlation in multivariate mixture models.

Keywords: Multivariate higher-degree increasing convex order; Ordering of mixtures; Parametric families of distributions; Upper orthant order; Orthant convex order; 60E15 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-015-0628-6

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