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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>

Latest revision as of 10:01, 9 August 2012

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