Log Gamma Distribution#
A single shape parameter c>0 . The support is x∈R.
f(x;c)=exp(cx−ex)Γ(c)F(x;c)=γ(c,ex)Γ(c)G(q;c)=log(γ−1(c,qΓ(c)))
where γ is the lower incomplete gamma function, γ(s,x)=∫x0ts−1e−tdt.
μ′n=∫∞0[logy]nyc−1exp(−y)dy.
μ=μ′1μ2=μ′2−μ2γ1=μ′3−3μμ2−μ3μ3/22γ2=μ′4−4μμ3−6μ2μ2−μ4μ22−3
Implementation: scipy.stats.loggamma