Loglogistic Distribution Example: Difference between revisions
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Determine the loglogistic parameter estimates for the data given in the following table. | Determine the loglogistic parameter estimates for the data given in the following table. | ||
<center><math>\overset{{}}{\mathop{\text{Test data}}}\,</math></center> | <center><math>\overset{{}}{\mathop{\text{Test data}}}\,\,\!</math></center> | ||
<center><math>\begin{matrix} | <center><math>\begin{matrix} | ||
Line 18: | Line 18: | ||
\text{9} & \text{675} & \text{680} \\ | \text{9} & \text{675} & \text{680} \\ | ||
\text{10} & \text{884} & \text{889} \\ | \text{10} & \text{884} & \text{889} \\ | ||
\end{matrix}</math></center> | \end{matrix}\,\!</math></center> | ||
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: | 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: | ||
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& {{{\hat{\mu }}}^{\prime }}= & 5.9772 \\ | & {{{\hat{\mu }}}^{\prime }}= & 5.9772 \\ | ||
& {{{\hat{\sigma }}}_{{{T}'}}}= & 0.3256 | & {{{\hat{\sigma }}}_{{{T}'}}}= & 0.3256 | ||
\end{align}</math> | \end{align}\,\!</math> | ||
For rank regression on <math>X\,\!</math>: | |||
For rank regression on | |||
::<math>\begin{align} | ::<math>\begin{align} | ||
& \hat{\mu }= & 5.9281 \\ | & \hat{\mu }= & 5.9281 \\ | ||
& \hat{\sigma }= & 0.3821 | & \hat{\sigma }= & 0.3821 | ||
\end{align}</math> | \end{align}\,\!</math> | ||
For rank regression on | For rank regression on <math>Y\,\!</math>: | ||
::<math>\begin{align} | ::<math>\begin{align} | ||
& \hat{\mu }= & 5.9772 \\ | & \hat{\mu }= & 5.9772 \\ | ||
& \hat{\sigma }= & 0.3256 | & \hat{\sigma }= & 0.3256 | ||
\end{align}</math> | \end{align}\,\!</math> |
Revision as of 17:51, 26 September 2012
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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.
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:
- [math]\displaystyle{ \begin{align} & {{{\hat{\mu }}}^{\prime }}= & 5.9772 \\ & {{{\hat{\sigma }}}_{{{T}'}}}= & 0.3256 \end{align}\,\! }[/math]
For rank regression on [math]\displaystyle{ X\,\! }[/math]:
- [math]\displaystyle{ \begin{align} & \hat{\mu }= & 5.9281 \\ & \hat{\sigma }= & 0.3821 \end{align}\,\! }[/math]
For rank regression on [math]\displaystyle{ Y\,\! }[/math]:
- [math]\displaystyle{ \begin{align} & \hat{\mu }= & 5.9772 \\ & \hat{\sigma }= & 0.3256 \end{align}\,\! }[/math]