Symmetric stable distribution (source code)

= Symmetric stable distribution
{title2=$\phi(t)=\exp(i\mu t-c|t|^\alpha),\quad0<\alpha\leq2$}

A symmetric stable distribution has this <characteristic function>, with $c>0$ and location $\mu$. At location zero it is a <strictly stable distribution>: weighted sums of <independent> copies have scale factor $(\sum_j|a_j|^\alpha)^{1/\alpha}$. The index $\alpha$ need not permit a finite <mean> or <variance>. The scale in this convention is $c^{1/\alpha}$, so the coefficient of $|t|^\alpha$ and the scale parameter should not be confused.