Template:LoglogisticDistribution: Difference between revisions

Latest revision as of 10:01, 9 August 2012

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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.
-<br>
-The <math>pdf</math> of the loglogistic distribution is given by:
-<br>
-::<math> \begin{align}
-   f(t)= & \frac{e^z}{\sigma_{t'}{(1+{e^z})^2}} \\
-   z= & \frac{t'-{\mu }'}{\sigma } \\
-f(t)\ge  & 0,t>0,{{\sigma }_{t'}}>0, \\
-  {t}'= & ln(t)
- \end{align}</math>
-<br>
-:where,
-<br>
-::<math>\begin{align}
- \mu'= & \text{scale parameter}  \\
-   \sigma_{t'}=& \text{shape parameter}
-\end{align}</math>
-<br>
-The loglogistic distribution and its characteristics are presented in more detail in Chapter 10.
-<br>