Theory of Statistics - George Mason University

836 Appendix A. Important Probability Distributions
Table A.6. Other Continuous Distributions (continued)
gamma PDF
α, β ∈ IR+ mean αβ
three-parameter gamma PDF
variance αβ 2
α, β ∈ IR+; γ ∈ IR mean αβ + γ
variance αβ 2
1
Γ(α)β αyα−1 e −y/β I ĪR+ (y)
exponential PDF θ −1 e −y/θ I ĪR+ (y)
θ ∈ IR+ mean θ
double exponential PDF
variance θ 2
µ ∈ IR; θ ∈ IR+ mean µ
(folded exponential) variance 2θ 2
Weibull PDF
1
Γ(α)β α(y − γ)α−1 e −(y−γ)/β I]γ,∞[(y)
1
2θ e−|y−µ|/θ
α
β yα−1 e −yα /β IĪR+ (y)
α, β ∈ IR+ mean β 1/α Γ(α −1 + 1)
extreme value (Type I) PDF
α ∈ IR; β ∈ IR+ mean α − βΓ ′ (1)
variance β 2/α ` Γ(2α −1 + 1) − (Γ(α −1 + 1)) 2´
1
β e−(y−α)/β exp(e −(y−α)/β )
variance β 2 π 2 /6
Theory of Statistics c○2000–2013 James E. Gentle