Template:Alta eyring-weibull: Difference between revisions

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==Eyring-Weibull==
#REDIRECT [[Eyring_Relationship#Eyring-Weibull]]
 
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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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{{eyring-weibull stat prop sum}}
 
===Parameter Estimation===
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{{eyring-weibull mle}}

Latest revision as of 23:13, 16 August 2012

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