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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]

[^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


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

vim: set ft=markdown:


Matlab code for fitting multidimensional t-distributions




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