ALTA ALTA Standard Folio Data PPH-Exponential: Difference between revisions

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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:  
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:  
<br>
<br>
::<math>{{\lambda }_{0}}(t)=\frac{\beta }{\eta }{{\left( \frac{t}{\eta } \right)}^{\beta -1}}</math>
<math>{{\lambda }_{0}}(t)=\frac{\beta }{\eta }{{\left( \frac{t}{\eta } \right)}^{\beta -1}}</math>
<br>
<br>
The PH failure rate  then becomes:  
The PH failure rate  then becomes:  
<br>
<br>
::<math>\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>
<math>\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>
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|  valign="middle" | [http://reliawiki.com/index.php/Template:PH_Model PH Model]
|  valign="middle" | [http://reliawiki.com/index.php/Template:PH_Model PH Model]

Revision as of 22:12, 10 February 2012

Webnotes-alta.png
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



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