TABLE 1.

Distributions

Model	Density	Distribution	Parameters
Weibull	$\frac{k}{\lambda }{\left(\frac{x}{\lambda }\right)}^{k-1}{e}^{-{\left(\frac{x}{\lambda }\right)}^k}$	$1-e^{{\left(\frac{x}{\lambda }\right)}^k}$	λ > 0; k > 0
Gompertz	$b\eta e^{bx+\eta -\eta e^{bx}}$	$1-e^{\eta -\eta e^{bx}}$	$\eta \in \mathcal{R}$; b > 0
Loglogistic	$\frac{(\beta /\alpha ){(x/\alpha )}^{\beta -1}}{{\left(1+{(x/\alpha )}^{\beta }\right)}^2}$	$\frac{1}{1+{(\alpha /x)}^{\beta }}$	α > 0; β > 0
Lognormal	$\frac{1}{x\sigma \sqrt{2\pi }}{e}^{-\frac{{(\text{ln}(x)-\mu )}^2}{2{\sigma }^2}}$	$\frac{1}{2}+\frac{1}{2}\mathrm{\Phi }\left(\frac{\text{ln}(x)-\mu }{\sqrt{2}\sigma }\right)$	$\mu \in \mathcal{R}$; σ > 0