Distribution Textbook (Work in Progress)

Part 0: Introduction

1. Introduction

Part I: Foundations

1. Probability
2. Probability II
3. Basic Statistics

Part II: Estimation

1. Parameters
2. Bounds
3. Estimators
4. Maximum Likelihood Estimation
   1. 2-D MLE Simulation
5. Method of Moments
6. Confidence Interval for Parameter Estimates
7. Empirical Distribution Function
   1. KS Test Simulator
   2. Two Sample KS Test Simulator
8. Goodness of Fit

Part III: Optimization

1. Introduction to Optimization
2. Multivariate Optimization
   1. Gradient Descent Simulation

Part IV: Sampling

1. Sampling (Continuous Distributions)
   1. Rejection Sampling Simulation
   2. Ziggurat Sampling Simulation
2. Sampling (Discrete)
   1. Multinomial Sampling Simulation
   2. Alias Sampling Simulation

Part V: Building More Complex Distributions

1. Extreme Value Theory
2. Mixture Distributions
3. Kernel Density Estimation
   1. 2-D KDE Simulation
4. Compound Distributions
5. Compound Poisson Distributions
6. Generalized Linear Models (GLM)
   1. Logistic Regression Visualizer
   2. Poisson Regression Visualizer
7. Modeling Zero-Inflated Data

Part VI: Bayesian Methods

1. Marginal Likelihood
2. Bayesian Inference
   1. Beta-Binomial Simulation
   2. Gamma-Poisson Simulation
3. Regularization

Part VII: Multivariate

1. Introduction to Multivariate Distributions
   1. Multivariate Distribution Visualizer
2. Distribution Distance
   1. Distribution Distance Visualizer
3. Dependence
   1. Kendall's Tau Visualizer
4. Combinations of Random Variables
   1. Convolution Visualizer
5. Copula
   1. Copula Visualizer
6. Random Matrices

Markov Chain Monte Carlo

1. Introduction to Markov Chains
2. Markov Chain Monte Carlo
3. Metropolis Algorithm
   1. Metropolis Visualizer
4. Introduction to Gibbs Sampling
   1. Gibbs Visualizer

Part VIII: Other

1. Stochastic Processes