Multivariate statistics is a form of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. The application of multivariate statistics is multivariate analysis. Multivariate statistics is concerned with understanding the different aims and background of each of the different forms of multivariate analysis and how they relate to each other. It is also concerned with multivariate probability distribution in terms of how these can be used to represent the distribution of observed data and how they can be used as part of statistical inference, where several different quantities are of interest to the same analysis.
There is a set of probability distribution used in multivariate analyses that plays a similar role to the corresponding set of distribution that are used in univariate analysis when the normal distribution is appropriate to a dataset. These are the multivariate normal distribution, the Wishart distribution and the Multivariate Student-t distribution.