Skewed & Heavy-Tailed Distributions for MATLAB

Skewed and heavy-tailed parametric distributions are widely used to model asymmetric data and tail-risk behaviour, particularly in applications such as modeling asset returns, and are commonly employed in Bayesian statistical frameworks. This repository brings together these and related parametric distributions in a consistent, MATLAB-compatible framework for the wider statistics community.

Each distribution is designed to:

• Integrate seamlessly with Statistics and Machine Learning Toolbox™
• Support PDF, CDF, ICDF, random generation, and fitting
• Be usable with standard MATLAB® functions such as:
  • makedist
  • fitdist
  • random
  • cdf, pdf, icdf
  • mean, var, std

The repository focuses on clarity, numerical stability, and compatibility with MATLAB's distribution framework. For detailed documentation please visit:

Documentation

or run

skewdoc 

Installation and setup

Requirements

• MATLAB® R2022b or newer (recommended)
• Statistics and Machine Learning Toolbox™

---

Get the latest version of the toolbox from releases.

Install by double-clicking on the file or:

matlab.addons.install("skewdists.mltbx") 

Once installed, run (once) the command below to refresh the Statistics and Machine Learning Toolbox with the new options:

makedist -reset 

Implemented Distributions

Distribution	Class Name
Epsilon-Skew-Normal	EpsilonSkewNormalDistribution
Inverse-Gamma	InverseGammaDistribution
Log-Gamma	LoggammaDistribution
Skew-Normal	SkewNormalDistribution
Split-Normal	SplitNormalDistribution
Skew-t	SkewTDistribution

---

Example Usage

% Create a distribution object
pd = makedist("SkewNormal", 0, 1, 5);

% Evaluate the PDF
x = linspace(-5, 5, 200);
y = pdf(pd, x);

% Random sampling
r = random(pd, 10000, 1);

% Fit a distribution to data
pdHat = fitdist(r, 'skewnormal');

% plot the fitted results
figure(Color = "w");
histogram(r, 100, Normalization = "pdf")
hold on; 
x = linspace(-1, 5, 200);
y = pdf(pdHat, x);
line(x, y, LineWidth = 2)

Repository Structure

├── README.md
├── SECURITY.md
├── License.txt
├── buildfile.m
├── tbx
│   ├── skewdist
|       ├── skewdoc
│       ├── +prob
│           ├── EpsilonSkewNormalDistribution.m
│           ├── InverseGammaDistribution.m
│           ├── LoggammaDistribution.m
│           ├── SkewNormalDistribution.m
│           ├── SplitNormalDistribution.m
│           └── SkewTDistribution.m
│   ├── doc
│      ├── EpsilonSkewNormalDistribution.md
│      ├── InverseGammaDistribution.md
│      ├── LoggammaDistribution.md
│      ├── SkewNormalDistribution.md
│      ├── SplitNormalDistribution.md
│      └── SkewTDistribution.md

• tbx/skewdist/+prob/*.m files contain the distribution class implementations.
• tbx/doc/ contains one Markdown file per distribution, documenting:
  • Mathematical definition
  • Parameters and constraints
  • Supported methods
  • Usage examples
  • Implementation notes

Contributing

Each new distribution should include:

1. A .m class file implementing the distribution
2. A corresponding documentation file in tbx/doc/
3. Full support for pdf, cdf, icdf, mean, var, std, fitdist, makedist