Univariate and Multivariate Normal Distributions

In this lecture we will look at the univariate, bivariate, and general multivariate Normal distributions. Structural Equation Models are based on an assumption that the responses have a multivariate Normal distribution. In addition, in Hierarchical Linear Models the random effects and model error term are assumed to be Normally distributed. So it will be helpful for us to be familiar with these families of distributions, the parameters in each family, and procedures for estimating the parameters for each type of Normal distribution.

We will look at the form of the pdf for each of these families of distributions and identify their various parameters.

Finally, we look at how to derive maximum-likelihood estimators for these parameters and how to obtain unbiased estimators of the parameters by adjusting those maximum-likelihood estimators that are biased.

Here is an outline of the topics in this lecture video:

The Normal (Gaussian) Distributions
Univariate Normal Distribution
Bivariate Normal Distribution
Multivariate Normal Distribution
Estimating the Parameters of the Univariate Normal Distribution
Estimating the Parameters of the Multivariate Normal Distribution

0:00 Introduction
1:02 Outline
1:59 Univariate Normal Distribution
11:27 Bivariate Normal Distribution
20:13 Multivariate Normal Distribution
26:57 Estimating the Parameters of the Univariate Normal Distribution
41:20 Estimating the Parameters of the Multivariate Normal Distribution
58:31 Outro