Gamma Distribution#
The standard form for the gamma distribution is (α>0) valid for x≥0 .
f(x;α)=1Γ(α)xα−1e−xF(x;α)=γ(α,x)Γ(α)G(q;α)=γ−1(α,qΓ(α))
where γ is the lower incomplete gamma function, γ(s,x)=∫x0ts−1e−tdt.
M(t)=1(1−t)α
μ=αμ2=αγ1=2√αγ2=6αmd=α−1
h[X]=Ψ(a)[1−a]+a+logΓ(a)
where
Ψ(a)=Γ′(a)Γ(a).
Implementation: scipy.stats.gamma