Table 2:

Possible choices of baseline hazard functions. f(t; λ, ρ) = λ(λt)^ρ−1e^−λt/Γ(ρ) is the density of gamma distribution; $S(t;\lambda ,\rho )=1-{\int }_0^{t}f(x;\lambda ,\rho )dx$ is the survival function of gamma distribution; ϕ and Φ are pdf and CDF of the standard normal distribution, respectively; for the piecewise constant hazard, 0 = τ₀ < τ₁ < ⋯ < τ_J = ∞, Δ_j(t) = 0 if t < τ_j−1, t − τ_j−1 if τ_j−1 ≤ t < τ_j, or τ_j − τ_j−1 if t ≥ τ_j, j = 1, …, J.

Distribution	Hazard h(t)	Cumulative hazard H (t)
Weibull	ρλ(λt)ρ−1	(λt)ρ	λ > 0 , ρ > 0
Log-logistic	$\frac{\rho \lambda {(\lambda t)}^{\rho -1}}{1+{(\lambda t)}^{\rho }}$	log{1 + (λt)ρ}	λ > 0 , ρ > 0
Log-normal	$\frac{\varphi \left\{(\text{log}t-\lambda )/\rho \right\}/(\rho t)}{\Phi \left\{-(\text{log}t-\lambda )/\rho \right\}}$	$-\text{log}\left\{\Phi \left(-\frac{\text{log}t-\lambda }{\rho }\right)\right\}$	−∞ < λ < ∞ , ρ > 0
Gompertz	$\lambda e^{\rho t}$	$\frac{\lambda }{\rho }\left(e^{\rho t}-1\right)$	λ > 0 , ρ > 0
Gamma	f (t; λ, ρ)/S(t; λ, ρ)	−log S(t; λ, ρ)	λ > 0 , ρ > 0
Log-Burr	$\frac{\rho \lambda \eta {(\lambda t)}^{\rho -1}}{\eta +{(\lambda t)}^{\rho }}$	η log{1 + (λt)ρ/η}	λ > 0 , ρ> 0 , η > 0
Piecewise constant	λi for t ∈ [τj−1, τj)	${\sum }_{j=1}^J{\lambda }_j{\Delta }_j(t)$	λj > 0 , j = 1,…, J