Cochran’s Theorem in Statistics: From Univariate to Multivariate Analysis

Cochran’s Theorem in Statistics: From Univariate to Multivariate Analysis

🔎 Introduction Cochran’s theorem is a cornerstone in statistical theory. It explains when quadratic forms of normal variables follow...

When Does a Quadratic Form Follow a Chi-Square Distribution?

When Does a Quadratic Form Follow a Chi-Square Distribution?

🔎 Motivation Quadratic forms arise in many statistical methods: Sample variance (measuring spread) Regression & ANOVA (part...

Multinomial Distribution: Theory, Applications, and a Real-World Example

Multinomial Distribution: Theory, Applications, and a Real-World Example

🔎 Introduction The multinomial distribution generalizes the binomial distribution to more than two outcomes. It is widely used in stati...