# How can I estimate the degrees of freedom for a Student's T distribution?

I am doing research estimating the value at risk for non-normally distributed assets. I need help in the process of estimating the parameters of Student's t distribution and which method to use. I would highly appreciate any assistance in this issue.

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Should this question perhaps be migrated to stats.SE? – Tal Fishman Aug 8 '11 at 3:22
Thank you for help. I will be thankful If you can be more detailed in the approach to the direct estimate method , Which software should I use for the estimation? Thanks – fariz Aug 8 '11 at 15:30

In software R use the function fitdistr ( package MASS). For more information: http://stat.ethz.ch/R-manual/R-patched/library/MASS/html/fitdistr.html

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Hi GrAra, welcome to quant.SE and thank you for your contribution. Please consider registering in order to track your answer and receive credit for your contributions to the site. – Tal Fishman Aug 9 '11 at 11:56

The pdfs of Student-t distributions have asymptotically Paretian tails, and the tail shape parameter (aka the maximal moment exponent) is equal to the distribution's degrees of freedom parameter. Assuming you have enough observations, you could estimate the Pareto parameter using the so-called Hill method (named after Bruce Hill, 1975). A word of caution: Use of the Hill method (and derived methods) is often criticized in fairly broad and rather unqualified ways. The main point to remember when using Hill's method is to use only observations that fall "safely" in the distribution's tails. Where this region lies differs from distribution to distribution. The only reasonably "safe" way is to plot the data in double-log coordinates: if the distribution does have Paretian tails, you'll see it in the graph, and you'll know where to set the cutoff for the observations that belong in the respective left and right tails.

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