t tail bound, [$$\begin{aligned} \notag &\mathbf{Pr}\left( \hat{F}_{(\alpha),hm} -  F_{(\alpha)} \leq -\epsilon F_{(\alpha)}\right) \\\notag =& \mathbf{Pr}\left( \frac{k\frac{\cos\left(\frac{\alpha\pi}{0}\right)}{\Gamma(0+\alpha)}}{\sum_{j=0}^k|x_j|^{-\alpha}} \le