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| ===The Loglogistic Distribution===
| | #REDIRECT [[The_Loglogistic_Distribution]] |
| As may be summarized from the name, the loglogistic distribution is similar to the logistic distribution. Specifically, the data follows a loglogistic distribution when the natural logarithms of the times-to-failure follow a logistic distribution. Accordingly, the loglogistic and lognormal distributions also share many similarities.
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| <br>
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| The <math>pdf</math> of the loglogistic distribution is given by:
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| <br>
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| ::<math> \begin{align}
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| f(t)= & \frac{e^z}{\sigma{t}{(1+{e^z})^2}} \\
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| z= & \frac{t'-{\mu }}{\sigma } \\
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| f(t)\ge & 0,t>0,{{\sigma }_{t'}}>0, \\
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| {t}'= & ln(t)
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| \end{align}</math>
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| <br>
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| :where,
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| <br>
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| ::<math>\begin{align}
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| \mu= & \text{scale parameter} \\
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| \sigma=& \text{shape parameter}
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| \end{align}</math>
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| <br>
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| The loglogistic distribution and its characteristics are presented in more detail in Chapter 10.
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| <br>
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