Student's t-Mixture Model

A Python implementation of "Robust mixture modelling using the t distribution" (Peel & McLachlan, 2000) and extensions.

Features

• Class StudentMixture: module for fitting a mixture of multivariate Student's t-distributions.
• Class MultivariateT: module for using a multivariate Student's t-random variable
• Class MultivaraiteTFit: module for fitting a multivariate Student's t-distribution.

Installation

With pip:

pip install student-mixture

From github:

git clone https://github.com/omritomer/student_mixture.git
cd student_mixture
python setup.py build
python setup.py install

Requirements

• numpy>=1.17.3
• scipy>=1.3.1
• scikit-learn>=1.5.0

References

1. Peel, D., & McLachlan, G. J. (2000). Robust mixture modelling using the t distribution. Statistics and computing, 10(4), 339-348.
2. McLachlan, G. J., & Peel, D. (2004). Finite mixture models. John Wiley & Sons.
3. McLachlan, G. J., & Krishnan, T. (2007). The EM algorithm and extensions (Vol. 382). John Wiley & Sons.
4. Genz, A., & Bretz, F. (2009). Computation of multivariate normal and t probabilities (Vol. 195). Springer Science & Business Media.
5. Genz, A. (2004). Numerical computation of rectangular bivariate and trivariate normal and t probabilities. Statistics and Computing, 14(3), 251-260.
6. Genz, A., & Bretz, F. (1999). Numerical computation of multivariate t-probabilities with application to power calculation of multiple contrasts. Journal of Statistical Computation and Simulation, 63(4), 103-117.
7. Genz, A., & Bretz, F. (2002). Comparison of methods for the computation of multivariate t probabilities. Journal of Computational and Graphical Statistics, 11(4), 950-971.
8. Kotz, S., & Nadarajah, S. (2004). Multivariate t-distributions and their applications. Cambridge University Press.

Citation

If you used this package to estimate a mixture of Student's t-distributions, please cite references 1 and 2, which this package is an implementation of.

If you used this package to estimate a Student's t-distribution, please cite reference 3.

The implementations mentioned above are structurally based on scikit-learn's mixture module, so please also cite scikit-learn according to their suggested format, which can be found here.

The implementations above are structurally based on scikit-learn's mixture module, so please also cite scikit-learn according to their suggested format, which can be found here.

If you used the multivariate Student's t-distribution module, please cite reference 8. As this module is structurally based on scipy's stats.multivariate module, please also cite scipy according to their suggested format, which can be found here.

If you used the cumulative distribution function (CDF) for either a multivariate t-distribution or a Student's t-mixture model, please cite reference 4. In addition, for the following cases:

• If your data has two or three dimensions, please cite reference 5.

• If your data has four or more dimensions, please cite references 6 and 7.

Authors

Omri Tomer (omritomer1990@gmail.com)

License

This package is distributed under the BSD 3-Clause License. See the LICENSE file for information.