Some alpha stable distribution documentation. (#6)

docs/alpha_stable.md

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+# Alpha-stable distribution modelling
+
+For any $alpha\in (0, 2]$, a centered alpha stable random variable $X$ has the following characteristic function
+$$exp(-|st|^\alpha)$$
+where $s$ is the scaling of $X$. If $\alpha=2$, it corresponds to a centered Gaussian distribution.
+
+If $X$ and $Y$ are independent alpha stable r.v., the sum $Z$ will satisfy:
+$$s_z^\alpha = s_x^\alpha + s_y^\alpha$$
+
+
+Some questions:
+* Is an alpha stable model more robust, i.e. better thanks to heavy tails representing outliers?
+* $alpha=1$, i.e. Cauchy distribution has the nice aspect of being very simple!
+
+
+## References
+
+* https://en.wikipedia.org/wiki/Stable_distribution
+* https://www.sciencedirect.com/topics/mathematics/stable-distribution