Loglogistic Distribution Example

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This example appears in the Life Data Analysis Reference book.

Determine the loglogistic parameter estimates for the data given in the following table.

\overset{{}}{\mathop{\text{Test data}}}\,\,\!
\begin{matrix}
   \text{Data point index} & \text{Last Inspected} & \text{State End time}  \\
   \text{1} & \text{105} & \text{106}  \\
   \text{2} & \text{197} & \text{200}  \\
   \text{3} & \text{297} & \text{301}  \\
   \text{4} & \text{330} & \text{335}  \\
   \text{5} & \text{393} & \text{401}  \\
   \text{6} & \text{423} & \text{426}  \\
   \text{7} & \text{460} & \text{468}  \\
   \text{8} & \text{569} & \text{570}  \\
   \text{9} & \text{675} & \text{680}  \\
   \text{10} & \text{884} & \text{889}  \\
\end{matrix}\,\!


Set up the folio for times-to-failure data that includes interval and left censored data, then enter the data. The computed parameters for maximum likelihood are calculated to be:

\begin{align}
  & {{{\hat{\mu }}}^{\prime }}= & 5.9772 \\ 
 & {{{\hat{\sigma }}}_{{{T}'}}}= & 0.3256  
\end{align}\,\!

For rank regression on X\,\!:

\begin{align}
  & \hat{\mu }= & 5.9281 \\ 
 & \hat{\sigma }= & 0.3821  
\end{align}\,\!

For rank regression on Y\,\!:

\begin{align}
  & \hat{\mu }= & 5.9772 \\ 
 & \hat{\sigma }= & 0.3256  
\end{align}\,\!
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