TracyWidom

Providing the Tracy-Widom distribution functions for beta = 1, 2, or 4 in Python.

This package uses the interpolation tables in

• Bejan, Andrei Iu. (2005), Largest eigenvalues and sample covariance matrices. Tracy–Widom and Painleve II: Computational aspects and realization in S-Plus with applications, M.Sc. dissertation, Department of Statistics, The University of Warwick.

and the asymptotics in

• Borot, Gaëtan and Nadal, Céline (2012), Right tail expansion of Tracy-Widom beta laws, Random Matrices: Theory and Applications Vol. 01, No. 03, 1250006. (arXiv:1111.2761)

This package is MIT licensed. If you use this package in your work, please consider citing the above publications and listing the URL of this package (https://github.com/yymao/TracyWidom/).

Installation

You can install tracywidom via conda or pip:

# Install via conda with the conda-forge channel
conda install tracywidom --channel conda-forge

# Or, install via pip
pip install tracywidom

Example

Here's an example of using the TracyWidom package.

import numpy as np
from TracyWidom import TracyWidom

x = np.linspace(-10, 10, 101)
tw1 = TracyWidom(beta=1)  # allowed beta values are 1, 2, and 4
pdf = tw1.pdf(x)
cdf = tw1.cdf(x)

r = np.random.rand(1000)
tw1_sample = tw1.cdfinv(r)