# The distribution of STD/MAD for a Student-t

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.

• This is a duplicate of the same question, by the same author, at: math.stackexchange.com/questions/602839/… – wolfies Dec 11 '13 at 17:53
• 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. – whuber Dec 11 '13 at 17:59
• 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. – Glen_b -Reinstate Monica Dec 11 '13 at 21:39
• @whuber I deleted in math sorry was unaware of the rules, thanks for the hlep. – Nero Dec 11 '13 at 23:23