Model

Parameter

f(t)

h(t)

S(t)

Exponential

$\lambda$

$\lambda \exp \left(-\lambda t\right)$

$\lambda$

$\exp \left(-\lambda t\right)$

Weibull

$\rho ,\lambda ={\eta }^{-\rho }$

$\lambda \rho t^{\rho -1}\exp \left(-\lambda t^{\rho }\right)$

$\lambda \rho t^{\rho -1}$

$\exp \left(-\lambda t^{\rho }\right)$

Lognormal

$\mu ,\tau$

$\frac{\sqrt{\tau }}{\sqrt{2\pi }t}\exp \left(-\frac{\tau }{2}{\left\{\ln \left(t\right)-\ln \left(\mu \right)\right\}}^2\right)$

$\frac{f\left(t\right)}{S\left(t\right)}$

$1-\Phi \left(\frac{\ln \left(t\right)-\mu }{1/\sqrt{\tau }}\right)$

Loglogistic

$\rho ,\lambda ={\mu }^{-\rho }$

$\frac{\lambda \rho t^{\rho -1}}{{\left(1+\lambda t^{\rho }\right)}^2}$

$\frac{\lambda \rho t^{\rho -1}}{1+\lambda t^{\rho }}$

$\frac{1}{1+\lambda t^{\rho }}$