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Math Help - weibull parameter

  1. #1
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    weibull parameter

    Hi All..

    I wanted to know how do you make the Weibull equation below into the form y=mx+c. The solution to this has the logs taken twice..

     P_f= 1 - exp\left[-\left(\frac{\sigma}{\sigma{_0}}\right)^m\right]

    Thank you
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  2. #2
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    Quote Originally Posted by dadon View Post
    Hi All..

    I wanted to know how do you make the Weibull equation below into the form y=mx+c. The solution to this has the logs taken twice..

     P_f= 1 - exp\left[-\left(\frac{\sigma}{\sigma{_0}}\right)^m\right]

    Thank you
    This is the cdf of the Weibull distribution. It's not clear to me what you're actually trying to do with it. Post the whole question, exactly as it's written.
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  3. #3
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    Hi.. thanks for your reply.. there is no question just from notes where the weibull is in the form y=mx+c.. just wanted to know the process on how it is derived?

    I will put the solution..
     \ln\ln\left(\frac{1}{1-P_f}\right) = m\ln\sigma - m\ln\sigma_0

    Thanks
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  4. #4
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    Hi dadon,

    We have
    P_f=1-exp\left[-\left(\frac{\sigma}{\sigma{_0}}\right)^m\right]

    Note that we can re-write this as

    exp\left[-\left(\frac{\sigma}{\sigma{_0}}\right)^m\right]=1-P_f

    Taking logs to the base e of both sides gives

    -\left(\frac{\sigma}{\sigma{_0}}\right)^m=\ln(1-P_f)


    Take the minus over to make it easier to deal with....

    \left(\frac{\sigma}{\sigma{_0}}\right)^m=-\ln(1-P_f)


    Now we know that a\ln(b)\equiv\ln(b^a) thus we are left with


    \left(\frac{\sigma}{\sigma{_0}}\right)^m=\ln\left(  \frac{1}{1-P_f}\right)

    Taking logs of base e again and using that same principle leads to


    <br />
m\ln\left[\left(\frac{\sigma}{\sigma{_0}}\right)\right]=\ln\left[\ln\left(\frac{1}{1-P_f}\right)\right]<br />

    Using the fact that \ln\left(\frac{a}{b}\right)\equiv \ln(a)-\ln(b) gives the required result.

    Hope this helps.
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    Thumbs up thanks

    Thank you.. that's exactly what I needed..You made it very clear line by line..
    Last edited by dadon; October 30th 2008 at 01:44 PM.
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