|
|
| (6 intermediate revisions by 3 users not shown) |
| Line 1: |
Line 1: |
| '''Lognormal Distribution General Example Complete Data'''
| | #REDIRECT [[The Lognormal Distribution]] |
| | |
| Determine the lognormal parameter estimates for the data given in Table 9.4.
| |
| {|align="center" border=1 cellspacing=1
| |
| |-
| |
| |colspan="3" style="text-align:center"| Table 9.4 - Non-Grouped Times-to-Failure Data
| |
| |-
| |
| !Data point index
| |
| !State F or S
| |
| !State End Time
| |
| |-
| |
| |1 ||F||2
| |
| |-
| |
| |2 ||F||5
| |
| |-
| |
| |3 ||F||11
| |
| |-
| |
| |4 ||F||23
| |
| |-
| |
| |5 ||F||29
| |
| |-
| |
| |6 ||F||37
| |
| |-
| |
| |7||F||43
| |
| |-
| |
| |8||F||59
| |
| |}
| |
| | |
| '''Solution'''
| |
| | |
| Using Weibull++, the computed parameters for maximum likelihood are:
| |
| | |
| ::<math>\begin{align}
| |
| & {{{\hat{\mu }}}^{\prime }}= & 2.83 \\
| |
| & {{{\hat{\sigma '}}}_}= & 1.10
| |
| \end{align}</math>
| |
| | |
| | |
| For rank regression on <math>X\ \ :</math>
| |
| | |
| ::<math>\begin{align}
| |
| & {{{\hat{\mu }}}^{\prime }}= & 2.83 \\
| |
| & {{{\hat{\sigma' }}}}= & 1.24
| |
| \end{align}</math>
| |
| | |
| | |
| For rank regression on <math>Y\ \ :</math>
| |
| | |
| ::<math>\begin{align}
| |
| & {{{\hat{\mu }}}^{\prime }}= & 2.83 \\
| |
| & {{{\hat{\sigma' }}}}= & 1.36
| |
| \end{align}</math>
| |