Gamma Distribution#

The standard form for the gamma distribution is (α>0) valid for x0 .

f(x;α)=1Γ(α)xα1exF(x;α)=γ(α,x)Γ(α)G(q;α)=γ1(α,qΓ(α))

where γ is the lower incomplete gamma function, γ(s,x)=x0ts1etdt.

M(t)=1(1t)α
μ=αμ2=αγ1=2αγ2=6αmd=α1
h[X]=Ψ(a)[1a]+a+logΓ(a)

where

Ψ(a)=Γ(a)Γ(a).

Implementation: scipy.stats.gamma