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| ==Eyring-Weibull==
| | #REDIRECT [[Eyring_Relationship#Eyring-Weibull]] |
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| <br>
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| The <math>pdf</math> for 2-parameter Weibull distribution is given by:
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| ::<math>f(t)=\frac{\beta }{\eta }{{\left( \frac{t}{\eta } \right)}^{\beta -1}}{{e}^{-{{\left( \tfrac{t}{\eta } \right)}^{\beta }}}}</math>
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| The scale parameter (or characteristic life) of the Weibull distribution is <math>\eta </math> . The Eyring-Weibull model <math>pdf</math> can then be obtained by setting <math>\eta =L(V)</math>:
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| ::<math>\eta =L(V)=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}</math>
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| or:
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| ::<math>\frac{1}{\eta }=V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}}</math>
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| Substituting for <math>\eta </math> into the Weibull <math>pdf</math> yields:
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| ::<math>f(t,V)=\beta \cdot V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}}{{\left( t\cdot V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}} \right)}^{\beta -1}}{{e}^{-{{\left( t\cdot V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}} \right)}^{\beta }}}}</math>
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| <br>
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| {{eyring-weibull stat prop sum}}
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| ===Parameter Estimation===
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| <br>
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| {{eyring-weibull mle}}
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