Computational statistics notes for simulation, random variable generation, Monte Carlo sanity checks, and probability-driven numerical methods.
Start Here
For statistical learning algorithms, use this section after the basic probability distribution tools.
- Generating Discrete Random Variables
- Generating Continuous Random Variables
- Box-Muller Transformation
Module Map
| Theme | Scope | Why it matters for statistical learning |
|---|---|---|
| Discrete simulation | Inverse transform and recursive CDF methods | Synthetic categorical/count data and sanity checks |
| Continuous simulation | Inverse transform and distribution transformations | Sampling continuous assumptions and transformed variables |
| Normal random variables | Box-Muller and normal simulation | Gaussian model checks, residual simulation, and CLT intuition |
Notes
| Area | Note | Status |
|---|---|---|
| Discrete simulation | Generating Discrete Random Variables | draft |
| Continuous simulation | Generating Continuous Random Variables | draft |
| Inverse transform | Generating Exponential Random Variables from Uniforms | draft |
| Inverse transform | Generating Geometric Random Variables from Uniforms | draft |
| Recursive CDF | Generating Poisson Random Variables from Uniforms | draft |
| Recursive CDF | Generating Binomial Random Variables from Uniforms | draft |
| Normal simulation | Box-Muller Transformation | draft |
Statistical Learning Use
- Generate synthetic data for sanity checks.
- Build Monte Carlo intuition for estimators and model assumptions.
- Connect sampling methods to uncertainty and probabilistic modeling.