On some counter examples of the bivariate and multivariate normal distributions: A brief survey

Abstract

We present some counterexamples of the classical and non-classical bivariate and multivariate normal distributions to widen our knowledge of these distributions. We hope that this paper will provide practitioners and users of bivariate and multivariate normal distributions of better view on the necessary and sufficient conditions leading to bivariate and multivariate normal distributions regarding marginal and or conditional distributions information.

Keywords:

• Classical bivariate and multivariate normal distribution
• nonstandard bivariate and multivariate normal distributions
• counterexamples

Acknowledgements

The authors are grateful to the referees as well as the Editor-in-Chief for making some constructive suggestions and comments on an earlier version of this manuscript which resulted in this much improved version.