Characterization of probability distributions

Characterization of probability distributions involves identifying the specific properties or features that define a particular statistical distribution. These characteristics provide a way to distinguish one distribution from another and can also help in the estimation or inference of the underlying random variables. Here are some fundamental aspects involved in the characterization of probability distributions: 1. **Moments**: Moments are expected values of powers of a random variable.

Cochran's theorem is a result in the field of statistics, particularly in the context of the analysis of variance (ANOVA) and the assessment of the independence of linear combinations of random variables. It is named after William G. Cochran. The theorem provides conditions under which the quadratic forms of a set of normally distributed random variables can be decomposed into independent components.