|
|
| (4 intermediate revisions by 3 users not shown) |
| Line 1: |
Line 1: |
| '''A Loglogistic Distribution Example'''
| | #REDIRECT [[Example:_Loglogistic_Distribution]] |
| | |
| Determine the loglogistic parameter estimates for the data given in Table 10.3.
| |
| | |
| <center><math>\overset{{}}{\mathop{\text{Table 10}\text{.3 - Test data}}}\,</math></center>
| |
| | |
| <center><math>\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></center>
| |
| | |
| | |
| Using Times-to-failure data under the Folio Data Type and the My data set contains interval and/or left censored data under Times-to-failure data options to enter the above data, the computed parameters for maximum likelihood are calculated to be:
| |
| | |
| ::<math>\begin{align}
| |
| & {{{\hat{\mu }}}^{\prime }}= & 5.9772 \\
| |
| & {{{\hat{\sigma }}}_{{{T}'}}}= & 0.3256
| |
| \end{align}</math>
| |
| | |
| | |
| For rank regression on <math>X\ \ :</math>
| |
| | |
| ::<math>\begin{align}
| |
| & \hat{\mu }= & 5.9281 \\
| |
| & \hat{\sigma }= & 0.3821
| |
| \end{align}</math>
| |
| | |
| | |
| For rank regression on <math>Y\ \ :</math>
| |
| | |
| ::<math>\begin{align}
| |
| & \hat{\mu }= & 5.9772 \\
| |
| & \hat{\sigma }= & 0.3256
| |
| \end{align}</math>
| |