Statistical Distributions

Explore a comprehensive series of lectures on statistical distributions, covering a wide range of topics from deriving the F distribution to understanding the distribution of the mid-range statistic. Delve into central and noncentral chi-square, t, and F distributions, as well as bivariate Poisson and normal distributions. Learn about the Wilcoxon signed-rank distribution, binomial distribution properties, and the Dirichlet distribution. Gain insights into specialized concepts such as the sample range, sample median, and the difference between binomial variables. Enhance your understanding of statistical theory and its practical applications through these in-depth, mathematically rigorous presentations.

Statistical Distributions: Derive the F Distribution.
Statistical Distributions: Noncentral Chi-square Distribution.
Statistical Distributions: Central & Noncentral Chi square df=1 Distributions.
Statistical Distributions: Central & Noncentral t Distributions.
Statistical Distributions: NonCentral Chi-sq as Sum of Chi-sq with Poisson Weights.
Statistical Distributions: NonCentral F Distribution.
Distribution of the Sample Range.
Distribution of the Sample Median.
Exact Distribution for the Difference between 2 Binomials Variables.
Derivation of the Bivariate Poisson Distribution.
Derivation of Bivariate Normal and the Conditional Distributions.
Integrating a Bivariate Normal Distribution.
Wilcoxon Signed Rank Distribution (Part 1).
Wilcoxon Signed Rank Distribution (Part 2).
Mean and Variance of a Binomial Distribution.
Non Normal Bivariate Distribution with Both Normal Marginals.
A df=1 noncentral chi sq distribution as a Poisson weighted mixture of central chi sq distributions.
Marginal Distribution of a Poisson Gamma Mixture Distribution.
Derivation of the Dirichlet Distribution.
Marginal Distributions of a Dirichlet Distribution.
Distribution of the Mid Range Statistic.