Template:LoglogisticDistribution: Difference between revisions

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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 <span class="texhtml">''pdf''</span> 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}}>0, \\
  {t}'= & ln(t) 
\end{align}</math>
 
<br>where,
 
::<math>\begin{align}
\mu= & \text{scale parameter}  \\
  \sigma=& \text{shape parameter}
\end{align}</math>
 
<br>The loglogistic distribution and its characteristics are presented in detail in [[The Loglogistic Distribution]]. <br>

Latest revision as of 10:01, 9 August 2012