Alpha Distribution¶
One shape parameters α>0 (parameter β in DATAPLOT is a scale-parameter). Standard form is x>0:
f(x;α)=1x2Φ(α)√2πexp(−12(α−1x)2)F(x;α)=Φ(α−1x)Φ(α)G(q;α)=[α−Φ−1(qΦ(α))]−1
M(t)=1Φ(a)√2π∫∞0extx2exp(−12(α−1x)2)dx
No moments?
lx(α)=Nlog[Φ(α)√2π]+2N¯logx+N2α2−α¯x−1+12¯x−2
Implementation: scipy.stats.alpha