Multivariate higher-degree stochastic increasing convexity

Building on the seminal work by Shaked and Shanthikumar (1988a,b), Denuit et al. (1999, 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},...,s_{d})-increasing convexity of distribution families indexed by a vector (Θ_{1}, θ_{2},..., θ_{d}) of parameters. This approach accounts for possible correlation in multivariate mixture models.