A First-Order Stein Characterization for Absolutely Continuous Bivariate Distributions
Document Type
Article
Publication Date
1-1-2023
Abstract
A random variable X has a standard normal distribution if and only if (Formula presented.) for any continuous and piecewise continuously differentiable function f such that the expectations exist. This first-order characterizing equation, called the Stein identity, has been extended to other univariate distributions. For the multivariate normal distribution, a number of Stein identities have already been developed, all of them second order equations. In this study, we developed a new Stein characterization for the bivariate normal distribution. Unlike many existing multivariate versions in the literature, ours is a system of first-order equations which has the univariate Stein identity as a special case. We also constructed a generalized Stein characterization for other absolutely continuous bivariate distributions. Finally, we illustrated how this Stein characterization looks like for some known absolutely continuous bivariate distributions.
Recommended Citation
Lester Charles A. Umali, Richard B. Eden & Timothy Robin Y. Teng (2023) A first-order Stein characterization for absolutely continuous bivariate distributions, Communications in Statistics - Theory and Methods, DOI: 10.1080/03610926.2023.2250485