Loglogistic Distribution Example: Difference between revisions
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[math]\displaystyle{ \overset{{}}{\mathop{\text{Test data}}}\,\,\! }[/math]
[math]\displaystyle{ \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}\,\! }[/math]
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{ | <noinclude>{{Banner Weibull Examples}} | ||
''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.</noinclude> | |||
< | |||
<center><math>\overset{{}}{\mathop{\text{ | Determine the loglogistic parameter estimates for the data given in the following table. | ||
<center><math>\overset{{}}{\mathop{\text{Test data}}}\,\,\!</math></center> | |||
<center><math>\begin{matrix} | <center><math>\begin{matrix} | ||
| Line 19: | 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: | |||
::<math>\begin{align} | ::<math>\begin{align} | ||
& {{{\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> | ||
Latest revision as of 21:39, 18 September 2023
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This example appears in the Life data analysis reference.
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]