Multivariate Higher-Degree Stochastic Increasing Convexity

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 $$(s_1,s_2,\ldots ,s_d)$$ -increasing convexity of distribution families indexed by a vector $$(\theta _1,\theta _2,\ldots ,\theta _d)$$ of parameters. This approach accounts for possible correlation in multivariate mixture models.