On generalized variance of product of powered components and multiple stable Tweedie models

ABSTRACT

A flexible family of multivariate models, named multiple stable Tweedie (MST) models, is introduced and produces generalized variance functions which are products of powered components of the mean. These MST models are built from a fixed univariate stable Tweedie variable having a positive value domain, and the remaining random variables given the fixed one are also real independent Tweedie variables, with the same dispersion parameter equal to the fixed component. In this huge family of MST models, generalized variance estimators are explicitly pointed out by maximum likelihood method and, moreover, computably presented for the uniform minimum variance and unbiased approach. The second estimator is brought from modified Lévy measures of MST which lead to some solutions of particular Monge–Ampère equations.

KEYWORDS:

• Generalized variance estimator
• Modified Lévy measure
• Multivariate exponential dispersion model
• α-Stable distribution.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E15
• 62F99

Acknowledgments

We sincerely thank the editor, the associate editor as well as an anonymous referee for their valuable comments and suggestions which led to significant improvement in this article.