Corrigendum to 'some gamma distributions' by Saralees Nadarajah

摘要

In 'Some Gamma Distributions' published in Statistics: A Journal of Theoretical and Applied Statistics, 2008;42(l):77-94 , the second author introduced a new generalized gamma probability density function (named as generalized gamma distribution) in the following form: f(x) = Cx~(α-1)(x + z)~(-ρ) exp (-λx) (1) for x ＞ 0, α ＞ 0, λ ＞ 0, z ＞ 0, and - ∞ ＜ ρ ＜ ∞, where C = C(α, λ, z, ρ) denotes a normalizing constant defined by 1/C(α,λ,z,ρ)=z~(α-ρ)Γ(α)Ψ(α, α+ 1 - ρ;λz) (2) and Ψ(a, b; u) denotes the confluent hypergeometric function defined by Ψ(a, b; u) = 1/Γ(α) ∫_0~∞ t~(α-1) (1 + t)~(b-a-1) exp (-ut) dt.