A multivariate Gaussian distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. A random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution.
Before looking at the multivariate Gaussian distribution, let's consider the univariate distribution.
A univariate distribution is generated with the following formula:
In the preceding formula, the following applies:
- σ represents the standard deviation of the distribution
- µ represents the mean of the distribution
Given the preceding two parameters, a Gaussian distribution with a certain mean and standard deviation is generated by varying the values of x from -∞ to ∞.
A typical plot of a Gaussian...
