Mathematical Background

Formal derivations for the distributions and algorithms in normix, based on Shi2016. Pages are grouped by topic. Bibliographic entries live in References.

Distributions

• The Generalized Inverse Gaussian Distribution
• The Generalized Hyperbolic Distribution
• Entropy, Varentropy, and Rényi Entropy

Fitting

• EM Algorithm for Generalized Hyperbolic Distributions
• Online EM Algorithm
• Shrinkage with Penalized Likelihood
• Factor Analysis for Generalized Hyperbolic Distributions

Portfolio & risk

• Mean-Risk Optimization for Normal Mixture Distributions
• CVaR Derivatives for Normal Mixture Distributions
• Portfolio Optimization with Transaction Costs
• Effective Number of Bets and Minimum Torsion
• Generalized Effective Number of Bets