Tutorials

Executable, end-to-end tutorials covering every public feature of normix. Each page runs against the current source at build time, so the code and outputs you see are always in sync with the library.

The tutorials are grouped into five tracks. Core builds the conceptual foundation; Distributions tours every class; EM covers fitting in practice; Statistics adds model comparison and goodness of fit; and Finance applies everything to real market data.

Formal derivations live in the Mathematical Background — tutorials pull in the key formulas where they help, and link out for the full math. Shrinkage remains theory-only until a matching tutorial lands.

Core concepts

• The exponential family
• A tour of the GH family
• Bessel functions and log_kv
• Random sampling

Distribution tour

• Univariate positive distributions
• The Generalized Inverse Gaussian
• The multivariate normal
• Normal variance-mean mixtures
• Factor mixtures for high dimensions

EM in practice

• Batch EM in practice
• Incremental (mini-batch) EM
• Initialization and multi-start
• EM vs MCECM Algorithm Comparison

Statistical analysis

• Divergences between models
• Goodness of fit
• Entropy, varentropy, and fat tails

Finance

• A heavy-tailed index series
• A multivariate stock basket
• Factor mixtures for a Dow Jones 30 portfolio
• Portfolio CVaR and its derivatives
• Mean-risk optimization and the efficient surface
• Transaction costs and local-quadratic rebalancing
• Diversification: variance ENB vs CVaR ENB