ALTA ALTA Standard Folio Data PPH-Exponential

Standard Folio Data PPH-Exponential

ALTA

A parametric form of the proportional hazards model can be obtained by assuming an underlying distribution. In ALTA PRO, the Weibull and exponential distributions are available. In this section we will consider the Weibull distribution to formulate the parametric proportional hazards model. In other words, it is assumed that the baseline failure rate in Eqn. (Prop. Failure Rate) is parametric and given by the Weibull distribution. In this case, the baseline failure rate is given by: [math]\displaystyle{ {{\lambda }_{0}}(t)=\frac{\beta }{\eta }{{\left( \frac{t}{\eta } \right)}^{\beta -1}} }[/math] The PH failure rate then becomes: [math]\displaystyle{ \lambda (t,\underline{X})=\frac{\beta }{\eta }{{\left( \frac{t}{\eta } \right)}^{\beta -1}}\cdot {{e}^{\mathop{}_{j=1}^{m}{{a}_{j}}{{x}_{j}}}} }[/math]

PH Model