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I'm going to generate a set of data from a T distribution and truncate the body(so that we make it approximately Pareto distributed) of it and estimate the tail exponent(shape parameter) of the truncated distribution. In the estimation process, I'm going to use different estimators for that. I need to know the exact(theoretical)value of alpha(tail exponent) in order to compare which method estimates the closest. So to obtain this theoretical alpha value, I need to know the relationship between df and alpha.

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They are the same. The tail of the Student's t is asymptotically Paretian with a tail exponent that is equal to df.

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  • $\begingroup$ Can you prove or explain tat, or at least add a reference? Otherwise it is a comment. $\endgroup$ – kjetil b halvorsen Mar 12 '19 at 12:49
  • $\begingroup$ @kjetilbhalvorsen we can generate some t distributed data with a known degrees of freedom and estimate the shape parameter for the tail and see it according to Tiana's answer. $\endgroup$ – Dovini Jayasinghe Mar 13 '19 at 9:38
  • $\begingroup$ @Dovini: That's a good idea Did you try? $\endgroup$ – kjetil b halvorsen Mar 13 '19 at 10:47
  • $\begingroup$ Yes I did, and it seems correct $\endgroup$ – Dovini Jayasinghe Mar 13 '19 at 11:02

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