5
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Where $X \sim a$ symmetric Student-t Distribution $t_\alpha$, with power law tail $\alpha>2$, looking for the distribution of

$$ \frac{\sqrt{ \sum_{i=1}^n x_i^2 }}{\sum_{i=1}^n |x_i|}, $$

in order to estimate the properties of the statistic STD/MAD for a sample size $n$.

The problem is that both measures, MAD and STD will be correlated for a given draw, so we cannot work with two different distributions.

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  • 1
    $\begingroup$ This is a duplicate of the same question, by the same author, at: math.stackexchange.com/questions/602839/… $\endgroup$ – wolfies Dec 11 '13 at 17:53
  • $\begingroup$ Nero, Because you first posted this message on the math site, I will close this copy (please ignore the stated reason). If you don't get any good answers there after a reasonable time, please flag it for attention and the math moderators will migrate it here. $\endgroup$ – whuber Dec 11 '13 at 17:59
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    $\begingroup$ This statistic is the inverse of Geary's 1935 $a$ statistic for testing normality against symmetric alternatives (with mean taken at zero). He considered its distribution, primarily in the normal case, e.g. see his 1947 paper where he considers; it may be worth considering using his statistic and approach. $\endgroup$ – Glen_b Dec 11 '13 at 21:39
  • $\begingroup$ @whuber I deleted in math sorry was unaware of the rules, thanks for the hlep. $\endgroup$ – Nero Dec 11 '13 at 23:23

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