|
|
| (4 intermediate revisions by 2 users not shown) |
| Line 1: |
Line 1: |
| '''Lognormal Distribution General Example Interval Data'''
| | #REDIRECT [[The_Lognormal_Distribution]] |
| | |
| Determine the lognormal parameter estimates for the data given in Table below.
| |
| {|align="center" border=1 cellspacing=1
| |
| |-
| |
| |colspan="3" style="text-align:center"| Table - Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)
| |
| |-
| |
| !Data point index
| |
| !Last Inspected
| |
| !State End Time
| |
| |-
| |
| |1 ||30||32
| |
| |-
| |
| |2 ||32||35
| |
| |-
| |
| |3 ||35||37
| |
| |-
| |
| |4 ||37||40
| |
| |-
| |
| |5 ||42||42
| |
| |-
| |
| |6 ||45||45
| |
| |-
| |
| |7||50||50
| |
| |-
| |
| |8||55||55
| |
| |}
| |
| | |
| '''Solution'''
| |
| | |
| This is a sequence of interval times-to-failure where the intervals vary substantially in length. Using Weibull++, the computed parameters for maximum likelihood are calculated to be:
| |
| | |
| ::<math>\begin{align}
| |
| & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\
| |
| & {{{\hat{\sigma }}}_{{{T}'}}}= & 0.18
| |
| \end{align}</math>
| |
| | |
| | |
| For rank regression on <math>X\ \ :</math>
| |
| | |
| ::<math>\begin{align}
| |
| & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\
| |
| & {{{\hat{\sigma }}}_{{{T}'}}}= & 0.17
| |
| \end{align}</math>
| |
| | |
| | |
| For rank regression on <math>Y\ \ :</math>
| |
| | |
| ::<math>\begin{align}
| |
| & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\
| |
| & {{{\hat{\sigma }}}_{{{T}'}}}= & 0.21
| |
| \end{align}</math>
| |