tdistfit

Some tools for fitting t-distributions to data.

EM methods

These methods find the maximum likelihood parameters using the expectation-maximization algorithm. Since I am fitting these distributions primarily to calculate entropy I am using covergence of entropy as a stopping criteria for the EM algorithm (rather than the full likelihood) but it is easy to change this if it is not suitable for your purposes.

• fitt : fits a multivariate t-distribution using ECME algorithm ¹
• fitt_fixnu : fits a t-distribution with d.o.f. (nu) specified.
• fitt_commonnu : fit t-distributions to grouped data, with d.o.f. (nu) common across groups
• fitt_commonsnu : fit t-distributions to grouped, with covariance (S) and d.o.f. (nu) common across groups

Approximate methods

These use a closed form approximation the ML estimate which is faster to compute. However, they didn't work well for me - with the data I was using I sometimes got negative values for terms which should be non-negative (although it seemed to work OK with generated t-distributed samples).

• fitt_approx : fits using the approximate method of Aeschliman et al. ²

License

This project is licensed under the GNU General Public License. For the exact terms please see the LICENSE file.

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Footnotes

1. C Liu and D B Rubin, (1995) "ML estimation of the t distribution using EM and its extensions, ECM and ECME", Statistica Sinica, 5, pp19-39 ↩

2. C Aeschlimna, J Park and KA Cak, "A Novel Parameter Estimation Algorithm for the Multivariate t-Distribution and its Application to Computer Vision" ECCV 2010 ↩