Template:LoglogisticDistribution: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
(Redirected page to The Loglogistic Distribution)
 
(10 intermediate revisions by 3 users not shown)
Line 1: Line 1:
===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=& \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