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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(α1x)2)F(x;α)=Φ(α1x)Φ(α)G(q;α)=[αΦ1(qΦ(α))]1
M(t)=1Φ(a)2π0extx2exp(12(α1x)2)dx

No moments?

lx(α)=Nlog[Φ(α)2π]+2N¯logx+N2α2α¯x1+12¯x2

Implementation: scipy.stats.alpha