A Complete Characterization of Multivariate Normal Stable Tweedie Models through a Monge Ampere Property  

作　　者：Célestin C.KOKONENDJI Cyrille C.MOYPEMNA SEMBONA Khoirin NISA 

机构地区：[1]Laboratoire de Mathematiques de Besancon(LMB)-Universite Bourgogne Franche-Comte,16,Route de Gray-25030 Besancon Cedex,Erance [2]Department of Mathematics and Informatics-University of Bangui,B.P.908 Bangui,Ceretrl African Repusblic [3]Departarert of Mathematics-Uriaersity of Lampung,Jl.Prof.Dr.Soemantri Brodjonegoro No.1 Bandar Lampung 35145,Indonesia

出　　处：《Acta Mathematica Sinica,English Series》2020年第11期1232-1244,共13页数学学报（英文版）

摘　　要：Extending normal gamma and normal inverse Gaussian models,multivariate normal stable Tweedie(NST)models are composed by a fixed univariate stable Tweedie variable having a positive value domain,and the remaining random variables given the fixed one are real independent Gaussian variables with the same variance equal to the fixed component.Within the framework of multivariate exponential families,the NST models are recently classified by their covariance matrices V(m)depending on the mean vector m.In this paper,we prove the characterization of all the NST models through their determinants of V(m),also called generalized variance functions,which are power of only one component of m.This result is established under the NST assumptions of Monge-Ampere property and steepness.It completes the two special cases of NST,namely normal Poisson and normal gamma models.As a matter of fact,it provides explicit solutions of particular Monge-Ampere equations in differential geometry.

关 键 词：Covariance matrix generalized variance function Monge-Ampere equation multivariateexponential family steepness 

分 类 号：O186.1[理学—数学]