Understanding Multivariate Normal Distribution

The math and intuition behind the multivariate normal distribution

The multivariate normal distribution is a generalization of the univariate normal distribution to two or more variables. It represents the distribution of a random vector containing multiple random variables that can be correlated with each other. The normal distribution is the most important distribution in statistics and probability theory, and since the multivariate normal distribution is a generalization of that, it also has a prominent role in statistics.

In this article, the math and intuition behind the multivariate normal distribution are discussed in detail. In addition, it will be shown how it can be modeled and implemented in Python using the Scipy library. Before we define the multivariate normal distribution, we need to review some important concepts like variance, covariance, and the covariance matrix. We also briefly review the univariate normal distribution. You can skip these sections if you are already familiar with them.

Variance and covariance

A random variable is a variable whose numerical value depends on the outcome of a random phenomenon. So, its value is initially unknown, but it becomes known once the outcome of the random phenomenon is realized. We commonly use uppercase letters to denote a…