Correction: A Novel Generalized Normal Distribution for Human Longevity and other Negatively Skewed Data.

In Table 1, the “Formula” column for “CDF” is incorrect. Please see the corrected Table 1 here.

Table 1

Properties of the distribution.

Quantity	Formula
Parameters	0 < σ < μ < λ
Domain	x є (0,λ)
PDF	f(x)=(1−μ/λ)Φ(μσ)2πσ(1−x/λ)^2exp{−(x−μ)^22σ^2(1−x/λ)^2}
CDF	F(x)=1−1−Φ(x−μσ(1−x/λ))Φ(μσ)
Hazard	(1-μ/λ)σ(1−x/λ)^2⋅ϕ[x−μσ(1−x/λ)]1−Φ[x−μσ(1−x/λ)]
Quantile	λ⋅μ−σΦ^−1[Φ(μσ)(1−p)]λ−σΦ^−1[Φ(μσ)(1−p)]
Median	μ−σΦ^-1[12Φ(μσ)]1−σλΦ^-1[12Φ(μσ)]≈μ
Mode	λ{1+(μ−λ)(−λ+λ^2+8σ^2)4σ^2}
Mean	∫0λx(1−μ/λ)Φ(μσ)2πσ(1−x/λ)^2exp{−(x−μ)^22σ^2(1−x/λ)^2}dx
Variance	∫0λ(x−E(X))^2(1−μ/λ)Φ(μσ)2πσ(1−x/λ)^2exp{−(x−μ)^22σ^2(1−x/λ)^2}dx