Parameter Values

Exponential Hazard Function:

\(\quad h(t)= \lambda\)

Plotted Function:



Parameter Values

Weibull Hazard Function:

\(\quad h(t)= \lambda p \left(\lambda t \right) ^{p - 1}\)

Plotted Function:



Parameter Values

Log-Normal Hazard Function:

\( \quad h(t)= \frac{\phi \left( \frac{ln(t)-\mu}{\sigma} \right)}{\sigma t \left[ 1-\Phi \left( \frac{ln(t)-\mu}{\sigma} \right) \right] } \)

Plotted Function:



Parameter Values

Log-Logistic Hazard Function:

\(\quad h(t)= \frac{\lambda^{-1} p \left(\lambda^{-1} t \right) ^{p - 1} } {1 + \left( \lambda^{-1} t \right)^{p} }\)

Plotted Function:



Parameter Values

Gompertz Hazard Function:

\(\quad h(t)= \lambda \exp \left( \gamma t \right) \)

Plotted Function:



Parameter Values

Generalized Gamma Hazard Function:

\( \quad h(t)= \frac{\phi \left( \frac{ln(t)-\mu}{\sigma} \right)}{\sigma t \left[ 1-\Phi \left( \frac{ln(t)-\mu}{\sigma} \right) \right] } \text{ when } \kappa = 0\)
\(\quad h(t)= \frac{\exp \left( -\ln \left( \sigma t \right) + \ln |\kappa| + \kappa^{-2} \ln \left( \kappa^{-2} \right) + \kappa^{-2} \left(\kappa * \frac{\ln \left( t \right) - \mu}{\sigma} - \exp \left( \kappa * \frac{\ln \left( t \right) - \mu}{\sigma} \right) \right) - \ln \left| \left( \Gamma \left( \kappa^{-2},t \right) \right) \right| \right)}{ S \left( t \right) } \)
where
\(\quad \Gamma \left(s, t \right) = \int_0^\infty t^{s-1} \exp \left( -t \right) dt \text{, the gamma function}\)
\(\quad S \left( t \right) = I_\Gamma \left( \kappa^{-2} \exp \left( \kappa * \frac{\ln \left( t \right) - \mu}{\sigma} \right), \kappa^{-2}, t\right) \text{ if } \kappa > 0 \)
\(\quad I_\Gamma \left(s,x,t \right) = \int_0^x t^{s-1} \exp \left( -t \right) dt \text{, the incomplete gamma function}\)
where
\(\quad \Gamma \left(s,t \right) = \int_0^\infty t^{s-1} \exp \left( -t \right) dt \text{, the gamma function}\)
\(\quad S \left( t \right) = 1 - I_\Gamma \left( \kappa^{-2} \exp \left( \kappa * \frac{\ln \left( t \right) - \mu}{\sigma} \right), \kappa^{-2}, t \right) \text{ if } \kappa \leq 0 \)
\(\quad I_\Gamma \left(s,x,t \right) = \int_0^x t^{s-1} \exp \left( -t \right) dt \text{, the incomplete gamma function}\)

Plotted Function: