Kokonendji, Célestin C. and MOYPEMNA SEMBONA, Cyrille C. and Nisa, Khoirin (2020) A Complete Characterization of Multivariate Normal Stable Tweedie Models through a Monge–Amp`ere Property. Acta Mathematica Sinica, English Series, 36 (11). pp. 1232-1244. ISSN 1439-8516

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Abstract

Abstract 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–Amp`ere 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–Amp`ere equations in differential geometry.

Item Type:	Article
Subjects:	H Social Sciences > HA Statistics
Divisions:	Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA) > Prodi Matematika
Depositing User:	DR. KHOIRIN NISA
Date Deposited:	11 Feb 2021 09:17
Last Modified:	11 Feb 2021 09:17
URI:	http://repository.lppm.unila.ac.id/id/eprint/27832

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